If the diagonals of a parallelogram are equal, the. show that it is a rectangle.
❌don't give irrelevant answers otherwise wrong answers will be reported ❌
Answers
Answer:
X
Take an online test Take Now
Login
Studyrankersonline
Ask a Question
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
0votes
6.9k views
asked Dec 22, 2017 in Class IX Maths by saurav24 Expert(1.4k points)
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Please log in or register to answer this question.
1 Answer
0votes
answered Dec 22, 2017 by navnit40 (-4,939 points)

Given : A parallelogram ABCD , in which AC = BD
TO Prove : ABCD is a rectangle .
Proof : In △ABC and △ABD
AB = AB [common]
AC = BD [given]
BC = AD [opp . sides of a | | gm]
⇒ △ABC ≅ △BAD [ by SSS congruence axiom]
⇒ ∠ABC = △BAD [c.p.c.t.]
Also, ∠ABC + ∠BAD = 180° [co - interior angles]
⇒ ∠ABC + ∠ABC = 180° [∵ ∠ABC = ∠BAD]
⇒ 2∠ABC = 180°
⇒ ∠ABC = 1 /2 × 180° = 90°
Hence, parallelogram ABCD is a rectangle
Answer is in attachment
