Construct a rhombus ABCD in which AB= 4 cm and angle ABC= 60degree Divide it into two triangle ABC - Maths - Constructions

Question

Construct a rhombus ABCD in which AB= 4 cm and angle ABC=
60 degree Divide it into two triangle ABC
and ADC Construct a triangle AB 'C ' similar to triangle ABC with
scale factor 2/3 Draw a line segment C 'D ' parallel to CD, where D
' lies on AD Is AB 'C 'D ' a rhombus? Give reasons

Chetna Khanna · Accepted Answer

Following are the steps of construction:
(1) Construct a line segment AB of length 4 cm.

(2) Construct an angle of 60° at B.

(3) From B cut an arc of length 4 cm and name it as C. Join BC.

(4) From C and A, mark arcs of lengths 4 cm. Let they intersect at a point say D.

(5) Join CD and AD.

ABCD is the required rhombus.

(6) Now, construct an acute angle on the downward side of A. Name it as AX.

(7) Mark three points X₁, X₂ and X₃ at equal distances on AX.

(8) Join X₃B and construct a line X₂B'parallel to X₃B.

(9) Construct B'C' parallel to BC and C'D' parallel AB.

AB'C'D' is the required rhombus.

Justification:

In ΔABC,

By BPT

$\frac{A B'}{A B} = \frac{A C'}{A C}$

Similarly, in ΔACD,

By BPT

$\frac{A D'}{A D} = \frac{A C'}{A C}$

Thus, we have $\frac{A B'}{A B} = \frac{A D'}{A D}$

As AB = CD

∴ AB'= CD'

Thus, AB'C'D' is a rhombus.

Justification: In Î”ABC, By BPT $\frac{A B'}{A B} = \frac{A C'}{A C}$ Similarly, in Î”ACD, By BPT $\frac{A D'}{A D} = \frac{A C'}{A C}$ Thus, we have $\frac{A B'}{A B} = \frac{A D'}{A D}$ As AB = CD âˆ´ AB'= CD' Thus, AB'C'D' is a rhombus

Construct a rhombus ABCD in which AB= 4 cm and angle ABC= 60 degree . Divide it into two triangle ABC and ADC. Construct a triangle AB 'C ' similar to triangle ABC with scale factor 2/3. Draw a line segment C 'D ' parallel to CD, where D ' lies on AD. Is AB 'C 'D ' a rhombus? Give reasons.

Construct a rhombus ABCD in which AB= 4 cm and angle ABC= 60 ^degree . Divide it into two triangle ABC and ADC. Construct a triangle AB 'C ' similar to triangle ABC with scale factor 2/3. Draw a line segment C 'D ' parallel to CD, where D ' lies on AD. Is AB 'C 'D ' a rhombus? Give reasons.