ABCD is a parallelogram. If its diagonals are equal, then find the value of ∠ABC.
Solution:
Consider a parallelogram
AB = CD and AD = BC
In ∆ABD and ∆ACB
AD = BC
BD = AC
AB = AB
From the SSS criterion
∆ABD ≅ ∆ACB
∠BAD = ∠ABC
We know that AD || BC and the transversal intersects them at A and B
∠BAD + ∠ABC = 180º
∠ABC + ∠ABC = 180º
2∠ABC = 180º
Dividing both sides by 2
∠ABC = 90º
Therefore, the value of ∠ABC is 90º.
✦ Try This: PQRS is a parallelogram. If its diagonals are equal, then find the value of ∠PQR.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8
NCERT Exemplar Class 9 Maths Exercise 8.2 Sample Problem 1
ABCD is a parallelogram. If its diagonals are equal, then find the value of ∠ABC
Summary:
ABCD is a parallelogram. If its diagonals are equal, then the value of ∠ABC is 90º
☛ Related Questions:
- Diagonals of a rhombus are equal and perpendicular to each other. Is this statement true? Give reaso . . . .
- Three angles of a quadrilateral ABCD are equal. Is it a parallelogram? Why or why not
- Diagonals AC and BD of a quadrilateral ABCD intersect each other at O such that OA : OC = 3: 2. Is A . . . .