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Syllabus
1) ACBD is a rectangle
2) CD is parallel to the original parallel lines.
1. AQ = BP
2. PQ = CD
3. ABPQ is a parallelogram
Q. In figure given below, ABCD is a rectangle and diagonals intersect at O. AC is produced to E. If ECD = 146, find the angles of triangle AOB.
Prove that : (i) MN = CD (ii) ABNM is a rhombus.
Q.7. (a) In figure (1) given below, equilateral triangle EBC surmounts square ABCD. Find angle BED represented by x.
(b) In figure (2) given below, ABCD is a rectangle and diagonals intersect at O. AC is produced to E. If ECD = 146, find the angles of the AOB.
(c) In figure (3) given below, ABCD is a rhombus and diagonals intersect at O. If OAB : OBA = 3 : 2, find the angles of the AOD.
18. In a parallelogram ABCD, the bisector of A meets DC in E and AB= 2AD. Prove that
(i) BE bisects B
(ii) AEB = a right angle.
14. (a) In figure ( 1) given below, A BCD is a parallelogram and X is mid-point of BC. The line AX produced meets DC produced at Q. The parallelogram ABPQ is completed. Prove that
(i) the triangles ABX and QCX are congruent-
(ii) DC=CQ=QP
Example 6. In the adjoining figure, ABCD is a parallelogram. Find the values of x, y and z.
Q.5. (a) In figure (1) given below, ABCD is a parallelogram with perimeter 40. Find the values of x and y.
(b) In figure (2) given below, ABCD is a parallelogram. Find the values of x and y.
(c) In figure (3) given below, ABCD is a rhombus. Find x and y.
Q10. In parallelogram ABCD, AP and AQ are perpendiculars from vertex of obtuse angle A as shown. If x : y = 2 : 1 ; find the angles of the parallelogram.
16. ABCD is a square. ABO is an equilateral triangle inside the square. Find DOC.
Q.8.c. In figure (3) given below, ABCD is a kite and diagonals intersect at O. If , find .
Q7. (a) In figure (1) given below, equilateral triangle EBC surmounts square ABCD. Find angle BED represented by x.
(b) In figure (2) given below, ABCD is a rectangle and diagonals intersect at O. AC is produced to E. If ECD = 146°, find the angles of the AOB.
(c) In figure (3) given below, ABCD is a rhombus and diagonals intersect at O. If OAB : OBA = 3 : 2, find the angles of the AOD.