RS Aggarwal 2019 Solutions for Class 8 Math Chapter 17 Construction Of Quadrilaterals are provided here with simple step-by-step explanations. These solutions for Construction Of Quadrilaterals are extremely popular among class 8 students for Math Construction Of Quadrilaterals Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RS Aggarwal 2019 Book of class 8 Math Chapter 17 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RS Aggarwal 2019 Solutions. All RS Aggarwal 2019 Solutions for class 8 Math are prepared by experts and are 100% accurate.
Page No 198:
Question 1:
Answer:
Steps of construction:
Step 1: Draw .
Step 2: With A as the centre and radius equal to , draw an arc.
Step 3: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as the centre and radius equal to draw an arc.
Step 6: With C as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.
Thus, ABCD is the required quadrilateral.
Page No 198:
Question 2:
Steps of construction:
Step 1: Draw .
Step 2: With A as the centre and radius equal to , draw an arc.
Step 3: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as the centre and radius equal to draw an arc.
Step 6: With C as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.
Thus, ABCD is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw .
Step 2: With P as the centre and radius equal to , draw an arc.
Step 3: With Q as the centre and radius equal to , draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to draw an arc.
Step 6: With R as the centre and radius equal to , draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.
Thus, PQRS is the required quadrilateral.
Page No 198:
Question 3:
Steps of construction:
Step 1: Draw .
Step 2: With P as the centre and radius equal to , draw an arc.
Step 3: With Q as the centre and radius equal to , draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to draw an arc.
Step 6: With R as the centre and radius equal to , draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.
Thus, PQRS is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw .
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With D as the centre and radius equal to draw an arc.
Step 6: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.
Thus, ABCD is the required quadrilateral.
Page No 198:
Question 4:
Steps of construction:
Step 1: Draw .
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With D as the centre and radius equal to draw an arc.
Step 6: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.
Thus, ABCD is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw .
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to draw an arc.
Step 6: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join AC, BC and CD.
Thus, ABCD is the required quadrilateral.
Page No 198:
Question 5:
Steps of construction:
Step 1: Draw .
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to draw an arc.
Step 6: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join AC, BC and CD.
Thus, ABCD is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw
Step 2: With Q as the centre and radius equal to , draw an arc.
Step 3: With R as the centre and radius equal to , draw another arc, cutting the previous arc at S.
Step 4: Join QS and RS.
Step 5: With S as the centre and radius equal to draw an arc.
Step 6: With R as the centre and radius equal to , draw another arc, cutting the previous arc at P.
Step 7: Join PS and PR.
Step 8: PQ = 4.9 cm
Thus, PQRS is the required quadrilateral.
Page No 198:
Question 6:
Steps of construction:
Step 1: Draw
Step 2: With Q as the centre and radius equal to , draw an arc.
Step 3: With R as the centre and radius equal to , draw another arc, cutting the previous arc at S.
Step 4: Join QS and RS.
Step 5: With S as the centre and radius equal to draw an arc.
Step 6: With R as the centre and radius equal to , draw another arc, cutting the previous arc at P.
Step 7: Join PS and PR.
Step 8: PQ = 4.9 cm
Thus, PQRS is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to draw an arc.
Step 6: With D as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join AC, CD and BC.
Thus, ABCD is the required quadrilateral.
Page No 198:
Question 7:
Steps of construction:
Step 1: Draw
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to draw an arc.
Step 6: With D as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join AC, CD and BC.
Thus, ABCD is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw AB= .
Step 2: Make .
Step 3: With B as the centre, draw an arc and name that point C.
Step 4: With C as the centre, draw an arc .
Step 5: With A as the centre, draw another arc â, cutting the previous arc at D.
Step 6: Join CD and AD.
Thus, is the required quadrilateral.
Page No 198:
Question 8:
Steps of construction:
Step 1: Draw AB= .
Step 2: Make .
Step 3: With B as the centre, draw an arc and name that point C.
Step 4: With C as the centre, draw an arc .
Step 5: With A as the centre, draw another arc â, cutting the previous arc at D.
Step 6: Join CD and AD.
Thus, is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw AB=
Step 2: Make
Step 3: With A as the centre, draw an arc of . Name that point as D.
Step 4: With D as the centre, draw an arc of .
Step 5: With B as the centre, draw an arc of 3.2 cm, cutting the previous arc at C.
Step 6: Join CD and BC.
Then, is the required quadrilateral.
Page No 198:
Question 9:
Steps of construction:
Step 1: Draw AB=
Step 2: Make
Step 3: With A as the centre, draw an arc of . Name that point as D.
Step 4: With D as the centre, draw an arc of .
Step 5: With B as the centre, draw an arc of 3.2 cm, cutting the previous arc at C.
Step 6: Join CD and BC.
Then, is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw BC=
Step 2: Make
Step 3: With B as the centre, draw an arc of . Name that point as A.
Step 4: With C as the centre, draw an arc of . Name that point as D.
Step 5: Join A and D.
Then, is the required quadrilateral.
Page No 198:
Question 10:
Steps of construction:
Step 1: Draw BC=
Step 2: Make
Step 3: With B as the centre, draw an arc of . Name that point as A.
Step 4: With C as the centre, draw an arc of . Name that point as D.
Step 5: Join A and D.
Then, is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw QR=
Step 2: Make
Step 3: With Q as the centre, draw an arc of . Name that point as P.
Step 4: With R as the centre, draw an arc of . Name that point as S.
Step 6: Join P and S.
Then, is the required quadrilateral.
Page No 198:
Question 11:
Steps of construction:
Step 1: Draw QR=
Step 2: Make
Step 3: With Q as the centre, draw an arc of . Name that point as P.
Step 4: With R as the centre, draw an arc of . Name that point as S.
Step 6: Join P and S.
Then, is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw AB=
Step 2: Make
Step 3: With B as the centre, draw an arc of .
Step 3: Sum of all the angles of the quadrilateral is .
Step 5: With C as the centre, make .
Step 6: Join C and D.
Step 7: Measure
Then, is the required quadrilateral.
Page No 199:
Question 12:
Steps of construction:
Step 1: Draw AB=
Step 2: Make
Step 3: With B as the centre, draw an arc of .
Step 3: Sum of all the angles of the quadrilateral is .
Step 5: With C as the centre, make .
Step 6: Join C and D.
Step 7: Measure
Then, is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw PQ=
Step 2:
Step 3: Make
Step 3: With Q as the centre, draw an arc of .
Step 4: Make
Step 6: Join R and S.
Step 7: Measure
Then, is the required quadrilateral.
Page No 199:
Question 13:
Steps of construction:
Step 1: Draw PQ=
Step 2:
Step 3: Make
Step 3: With Q as the centre, draw an arc of .
Step 4: Make
Step 6: Join R and S.
Step 7: Measure
Then, is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw
Step 2:
Step 3:
With B as the centre, draw an arc equal to 3 cm.
Step 4: Make
Step 5: With A as the centre and radius equal to , draw an arc and name that point as D.
Then, is the required quadrilateral.
Page No 201:
Question 1:
Steps of construction:
Step 1: Draw
Step 2:
Step 3:
With B as the centre, draw an arc equal to 3 cm.
Step 4: Make
Step 5: With A as the centre and radius equal to , draw an arc and name that point as D.
Then, is the required quadrilateral.
Answer:
Steps of construction:
Step 1: Draw AB =
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , cutting the previous arc at C.
Step 4: Join A and C.
Step 5: We know that the opposite sides of a parallelogram are equal. Thus, with C as the centre, draw an arc of .
Step 6: With A as the centre, draw another arc of , cutting the previous arc at D.
Step 7: Join CD and AD.
Then, ABCD is the required parallelogram.
Page No 201:
Question 2:
Steps of construction:
Step 1: Draw AB =
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , cutting the previous arc at C.
Step 4: Join A and C.
Step 5: We know that the opposite sides of a parallelogram are equal. Thus, with C as the centre, draw an arc of .
Step 6: With A as the centre, draw another arc of , cutting the previous arc at D.
Step 7: Join CD and AD.
Then, ABCD is the required parallelogram.
Answer:
Steps of construction:
Step 1: Draw AB=
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: We know that the opposite sides of a parallelogram are equal.
Thus, with D as the centre, draw an arc of .
Step 6: With B as the centre, draw another arc of , cutting the previous arc at C.
Step 7: Join CD and BC.
âthen, ABCD is the required parallelogram.
Page No 201:
Question 3:
Steps of construction:
Step 1: Draw AB=
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: We know that the opposite sides of a parallelogram are equal.
Thus, with D as the centre, draw an arc of .
Step 6: With B as the centre, draw another arc of , cutting the previous arc at C.
Step 7: Join CD and BC.
âthen, ABCD is the required parallelogram.
Answer:
Steps of construction:
Step 1: Draw PQ= 4 cm
Step 2: Make
Step 2: With Q as the centre, draw an arc of 6 cm and name that point as R.
Step 3: With R as the centre, draw an arc of 4 cm and name that point as S.
Step 4: Join SR and PS.
Then, PQRS is the required parallelogram.
Page No 201:
Question 4:
Steps of construction:
Step 1: Draw PQ= 4 cm
Step 2: Make
Step 2: With Q as the centre, draw an arc of 6 cm and name that point as R.
Step 3: With R as the centre, draw an arc of 4 cm and name that point as S.
Step 4: Join SR and PS.
Then, PQRS is the required parallelogram.
Answer:
Steps of construction:
Step 1: Draw BC=
Step 2: Make an
Step 2: With C as centre draw an arc of , name that point as D
Step 3: With D as centre draw an arc , name that point as A
Step 4: With B as centre draw another arc cutting the previous arc at A.
Step 5: Join AD and AB
âthen, ABCD is a required parallelogram.
Page No 201:
Question 5:
Steps of construction:
Step 1: Draw BC=
Step 2: Make an
Step 2: With C as centre draw an arc of , name that point as D
Step 3: With D as centre draw an arc , name that point as A
Step 4: With B as centre draw another arc cutting the previous arc at A.
Step 5: Join AD and AB
âthen, ABCD is a required parallelogram.
Answer:
We know that the diagonals of a parallelogram bisect each other.
Steps of construction:
Step 1: Draw AB=
Step 2: With A as the centre and radius , draw an arc.
Step 3: With B as the centre and radius , draw another arc, cutting the previous arc at point O.
Step 4: Join OA and OB.
Step 5: Produce OA to C, such that OC= AO. Produce OB to D, such that OB=OD.
Step 5: Join AD, BC, and CD.
Thus, ABCD is the required parallelogram. The other side is 4.5 cm in length.
Page No 201:
Question 6:
We know that the diagonals of a parallelogram bisect each other.
Steps of construction:
Step 1: Draw AB=
Step 2: With A as the centre and radius , draw an arc.
Step 3: With B as the centre and radius , draw another arc, cutting the previous arc at point O.
Step 4: Join OA and OB.
Step 5: Produce OA to C, such that OC= AO. Produce OB to D, such that OB=OD.
Step 5: Join AD, BC, and CD.
Thus, ABCD is the required parallelogram. The other side is 4.5 cm in length.
Answer:
Steps of construction:
Step 1: Draw AB= 6.5cm
Step 2: Draw a perpendicular at point A. Name that ray as AX. From point A, draw an arc of length 2.5 cm on the ray AX and name that point as L.
Step 3: On point L, make a perpendicular. Draw a straight line YZ passing through L, which is perpendicular to the ray AX.
Step 4: Cut an arc of length 3.4 cm on the line YZ and name it as C.
Step 5: From point C, cut an arc of length 6.5 cm on the line YZ. Name that point as D.
Step 6: Join BC and AD.
Therefore, quadrilateral ABCD is a parallelogram.
The altitude from C measures 2.5 cm in length.
Page No 201:
Question 7:
Steps of construction:
Step 1: Draw AB= 6.5cm
Step 2: Draw a perpendicular at point A. Name that ray as AX. From point A, draw an arc of length 2.5 cm on the ray AX and name that point as L.
Step 3: On point L, make a perpendicular. Draw a straight line YZ passing through L, which is perpendicular to the ray AX.
Step 4: Cut an arc of length 3.4 cm on the line YZ and name it as C.
Step 5: From point C, cut an arc of length 6.5 cm on the line YZ. Name that point as D.
Step 6: Join BC and AD.
Therefore, quadrilateral ABCD is a parallelogram.
The altitude from C measures 2.5 cm in length.
Answer:
We know that the diagonals of a parallelogram bisect each other.
Steps of construction:
Step 1: Draw AC=
Step 2: Bisect AC at O.
Step 3: Make
Produce XO to Y.
Step 4:
Step 5: Join AB, BC, CD and AD.
âThus, ABCD is the required parallelogram.
Page No 201:
Question 8:
We know that the diagonals of a parallelogram bisect each other.
Steps of construction:
Step 1: Draw AC=
Step 2: Bisect AC at O.
Step 3: Make
Produce XO to Y.
Step 4:
Step 5: Join AB, BC, CD and AD.
âThus, ABCD is the required parallelogram.
Answer:
Steps of construction:
Step 1: Draw AB =
Step 2: Make
Step 3: Draw an arc of 8.5 cm from point A and name that point as D.
Step 4: Draw an arc of 8.5 cm from point B and name that point as C.
Step 5: Join C and D.
Thus, ABCD is the required rectangle.
Page No 201:
Question 9:
Steps of construction:
Step 1: Draw AB =
Step 2: Make
Step 3: Draw an arc of 8.5 cm from point A and name that point as D.
Step 4: Draw an arc of 8.5 cm from point B and name that point as C.
Step 5: Join C and D.
Thus, ABCD is the required rectangle.
Answer:
All the sides of a square are equal.
Steps of construction:
Step 1: Draw AB =
Step 2: Make
Step 3: Draw an arc of length 6.4 cm from point A and name that point as D.
Step 4: Draw an arc of length 6.4 cm from point B and name that point as C.
Step 5: Join C and D.
âThus, ABCD is a required square.
Page No 201:
Question 10:
All the sides of a square are equal.
Steps of construction:
Step 1: Draw AB =
Step 2: Make
Step 3: Draw an arc of length 6.4 cm from point A and name that point as D.
Step 4: Draw an arc of length 6.4 cm from point B and name that point as C.
Step 5: Join C and D.
âThus, ABCD is a required square.
Answer:
We know that the diagonals of a square bisect each other at right angles.
Steps of construction:
Step 1: Draw AC=
Step 2: Draw the perpendicular bisector XY of AC, meeting it at O.
Step 3:
:
Step 4: Join AB, BC, CD and DA.
ABCD is the required square.
Page No 201:
Question 11:
We know that the diagonals of a square bisect each other at right angles.
Steps of construction:
Step 1: Draw AC=
Step 2: Draw the perpendicular bisector XY of AC, meeting it at O.
Step 3:
:
Step 4: Join AB, BC, CD and DA.
ABCD is the required square.
Answer:
Steps of construction:
Step 1: Draw QR =
Step 2: Make
Step 3:
Step 3: Draw an arc of length 4.8 cm from point Q and name that point as P.
âStep 4: Draw an arc of length 6 cm from point R, cutting the previous arc at P.
âStep 5: Join PQ
Step 6: Draw an arc of length 4.8 cm from point R.
From point P, draw an arc of length 3.6 cm, cutting the previous arc. Name that point as S.
Step 7: Join P and S.
Thus, PQRS is the required rectangle. The other side is 4.8 cm in length.
Page No 201:
Question 12:
Steps of construction:
Step 1: Draw QR =
Step 2: Make
Step 3:
Step 3: Draw an arc of length 4.8 cm from point Q and name that point as P.
âStep 4: Draw an arc of length 6 cm from point R, cutting the previous arc at P.
âStep 5: Join PQ
Step 6: Draw an arc of length 4.8 cm from point R.
From point P, draw an arc of length 3.6 cm, cutting the previous arc. Name that point as S.
Step 7: Join P and S.
Thus, PQRS is the required rectangle. The other side is 4.8 cm in length.
Answer:
We know that the diagonals of a rhombus bisect each other.
.Steps of construction:
Step 1: Draw AC=
Step 2:Draw a perpendicular bisector(XY) of AC, which bisects AC at O.
Step 3:
Draw an arc of length 4 cm on OX and name that point as B.
Draw an arc of length 4 cm on OY and name that point as D.
Step 4 : Join AB, BC, CD and AD.
âThus, ABCD is the required rhombus, as shown in the figure.
Page No 201:
Question 13:
We know that the diagonals of a rhombus bisect each other.
.Steps of construction:
Step 1: Draw AC=
Step 2:Draw a perpendicular bisector(XY) of AC, which bisects AC at O.
Step 3:
Draw an arc of length 4 cm on OX and name that point as B.
Draw an arc of length 4 cm on OY and name that point as D.
Step 4 : Join AB, BC, CD and AD.
âThus, ABCD is the required rhombus, as shown in the figure.
Answer:
Steps of construction:
Step 1: Draw AB =
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , cutting the previous arc at C.
âStep 4: Join AC and BC.
Step 5: With C as the centre, draw an arc of 4 cm.
Step 6: âWith A as the centre, draw another arc of , cutting the previous arc at D.
Step 7: Join AD and CD.
ABCD is the required rhombus.
Page No 201:
Question 14:
Steps of construction:
Step 1: Draw AB =
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , cutting the previous arc at C.
âStep 4: Join AC and BC.
Step 5: With C as the centre, draw an arc of 4 cm.
Step 6: âWith A as the centre, draw another arc of , cutting the previous arc at D.
Step 7: Join AD and CD.
ABCD is the required rhombus.
Answer:
Steps of construction:
Step1: Draw AB =
Step2: Draw
Sum of the adjacent angles is 180°.
Step 3:
Step 4: Join C and D.
Then, ABCD is the required rhombus.
Page No 201:
Question 15:
Steps of construction:
Step1: Draw AB =
Step2: Draw
Sum of the adjacent angles is 180°.
Step 3:
Step 4: Join C and D.
Then, ABCD is the required rhombus.
Answer:
Steps of construction:
Step 1: Draw AB=
Step 2: Make
Step 3: With B as the centre, draw an arc at . Name that point as C.
Step 4:
Make
At C, draw an arc of length .
Step 5: Join A and D.
Thus, ABCD is the required trapezium.
Page No 201:
Question 16:
Steps of construction:
Step 1: Draw AB=
Step 2: Make
Step 3: With B as the centre, draw an arc at . Name that point as C.
Step 4:
Make
At C, draw an arc of length .
Step 5: Join A and D.
Thus, ABCD is the required trapezium.
Answer:
Steps of construction :
Step1: Draw AB equal to 7 cm.
Step2: Make an angle,
Step3: With B as the centre, draw an arc of . Name that point as C. Join B and C.
Step4:
Draw an angle,
Step4: With A as the centre, draw an arc of length , which cuts CY. Mark that point as D.
Step5: Join A and D.
âThus, ABCD is the required trapezium.
Page No 202:
Question 1:
Steps of construction :
Step1: Draw AB equal to 7 cm.
Step2: Make an angle,
Step3: With B as the centre, draw an arc of . Name that point as C. Join B and C.
Step4:
Draw an angle,
Step4: With A as the centre, draw an arc of length , which cuts CY. Mark that point as D.
Step5: Join A and D.
âThus, ABCD is the required trapezium.
Answer:
( i) Open curve: An open curve is a curve where the beginning and end points are different.
Example: Parabola
(ii) Closed Curve: A curve that joins up so there are no end points.
Example: Ellipse
(iii) Simple closed curve: A closed curve that does not intersect itself.
Page No 202:
Question 2:
( i) Open curve: An open curve is a curve where the beginning and end points are different.
Example: Parabola
(ii) Closed Curve: A curve that joins up so there are no end points.
Example: Ellipse
(iii) Simple closed curve: A closed curve that does not intersect itself.
Answer:
Let the angles be
Sum of the angles of a quadrilateral is .
The angles of the quadrilateral are
Page No 202:
Question 3:
Let the angles be
Sum of the angles of a quadrilateral is .
The angles of the quadrilateral are
Answer:
Sum of any two adjacent angles of a parallelogram is .
Measures of the angles are .
Page No 202:
Question 4:
Sum of any two adjacent angles of a parallelogram is .
Measures of the angles are .
Answer:
Let the length be cm and the breadth be cm.
Perimeter of the rectangle =180
Perimeter of the rectangle=
Page No 202:
Question 5:
Let the length be cm and the breadth be cm.
Perimeter of the rectangle =180
Perimeter of the rectangle=
Answer:
Rhombus is a parallelogram.
Therefore, the diagonals bisects at O.
Now, let us prove that the diagonals intersect each other at right angles.
Consider :
∴
∴ (corresponding parts of congruent triangles)
Further,
∴
It is proved that the diagonals of a rhombus are perpendicular bisectors of each other.
Page No 202:
Question 6:
Rhombus is a parallelogram.
Therefore, the diagonals bisects at O.
Now, let us prove that the diagonals intersect each other at right angles.
Consider :
∴
∴ (corresponding parts of congruent triangles)
Further,
∴
It is proved that the diagonals of a rhombus are perpendicular bisectors of each other.
Answer:
All the sides of a rhombus are equal in length.
The diagonals of a rhombus intersect at .
The diagonal and the side of a rhombus form right triangles.
In :
Therefore, the length of each side of the rhombus is 10 cm.
Page No 202:
Question 7:
All the sides of a rhombus are equal in length.
The diagonals of a rhombus intersect at .
The diagonal and the side of a rhombus form right triangles.
In :
Therefore, the length of each side of the rhombus is 10 cm.
Answer:
(b) 37o, 143o, 37o 143o
Opposite angles of a parallelogram are equal.
Therefore, the first and the second angles are:
Sum of adjacent angles in a parallelogram is .
Adjacent angles =
Page No 202:
Question 8:
(b) 37o, 143o, 37o 143o
Opposite angles of a parallelogram are equal.
Therefore, the first and the second angles are:
Sum of adjacent angles in a parallelogram is .
Adjacent angles =
Answer:
(d) none of the these
Let the angles be .
Sum of the angles of the quadrilateral is .
Page No 202:
Question 9:
(d) none of the these
Let the angles be .
Sum of the angles of the quadrilateral is .
Answer:
(b) 6 cm
Let the breadth of the rectangle be x cm.
Diagonal =10 cm
Length= 8 cm
The rectangle is divided into two right triangles.
Breadth of the rectangle = 6 cm
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Question 10:
(b) 6 cm
Let the breadth of the rectangle be x cm.
Diagonal =10 cm
Length= 8 cm
The rectangle is divided into two right triangles.
Breadth of the rectangle = 6 cm
Answer:
(d) x = 8
All sides of a square are equal.
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Question 11:
(d) x = 8
All sides of a square are equal.
Answer:
(d) 90°
We know that the opposite sides and the angles in a parallelogram are equal.
Also, its adjacent sides are supplementary, i.e. sum of the sides is equal to 180.
Now, the bisectors of these angles form a triangle, whose two angles are:
Hence, the two bisectors intersect at right angles.
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Question 12:
(d) 90°
We know that the opposite sides and the angles in a parallelogram are equal.
Also, its adjacent sides are supplementary, i.e. sum of the sides is equal to 180.
Now, the bisectors of these angles form a triangle, whose two angles are:
Hence, the two bisectors intersect at right angles.
Answer:
(c) 9
Hexagon has six sides.
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Question 13:
(c) 9
Hexagon has six sides.
Answer:
(b) 8
It has 8 sides.
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Question 14:
(b) 8
It has 8 sides.
Answer:
(i) Sum of all exterior angles =
(ii) Sum of all interior angles =
(iii) Number of diagonals =
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Question 15:
(i) Sum of all exterior angles =
(ii) Sum of all interior angles =
(iii) Number of diagonals =
Answer:
(i) Sum of all exterior angles of a regular polygon is .
(ii) Sum of all interior angles of a polygon is
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Question 16:
(i) Sum of all exterior angles of a regular polygon is .
(ii) Sum of all interior angles of a polygon is
Answer:
(i) Octagon has 8 sides.
(ii) Sum of the interior angles of a regular hexagon =
(iii) Each exterior angle of a regular polygon is .
Therefore, the given polygon is a hexagon.
(iv) If the interior angle is , then the exterior angle will be . (interior and exterior angles are supplementary)
Sum of the exterior angles of a polygon is 360°.
Let there be n sides of a polygon.
Since it has 5 sides, the polygon is a pentagon.
(v) A pentagon has 5 diagonals.
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Question 17:
(i) Octagon has 8 sides.
(ii) Sum of the interior angles of a regular hexagon =
(iii) Each exterior angle of a regular polygon is .
Therefore, the given polygon is a hexagon.
(iv) If the interior angle is , then the exterior angle will be . (interior and exterior angles are supplementary)
Sum of the exterior angles of a polygon is 360°.
Let there be n sides of a polygon.
Since it has 5 sides, the polygon is a pentagon.
(v) A pentagon has 5 diagonals.
Answer:
(i) F
The diagonals of a parallelogram need not be equal in length.
(ii) F
The diagonals of a rectangle are not perpendicular to each other.
(iii) T
(iv) T
Adjacent sides of a kite are equal and this is also true for a rhombus. Additionally, all the sides of a rhombus are equal to each other.
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Question 18:
(i) F
The diagonals of a parallelogram need not be equal in length.
(ii) F
The diagonals of a rectangle are not perpendicular to each other.
(iii) T
(iv) T
Adjacent sides of a kite are equal and this is also true for a rhombus. Additionally, all the sides of a rhombus are equal to each other.
Answer:
Steps of construction:
Step 1: Take PQ = 4.2 cm
Step 2:
Step 3: Cut an arc of length 5 cm from point Q. Name that point as R.
Step 4: From P, make an arc of length 6 cm. Name that point as S.
Step 5: Join P and S.
Thus, PQRS is a quadrilateral.
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