Question

Part 2
11. Prove that angles opposite to equal sides of an isosceles triangle are equal.
12. Prove that a diagonal of parallelogram divides it into two congruent triangles.​

Answer 1

Answer:

Step-by-step explanation:

. Prove that a diagonal of parallelogram divides it into two congruent triangles.​ so answer is 80degere

Answer 2

Answer:

11.Let △ABC be an isosceles triangle such that AB =AC Then we have to prove that ∠B=∠C Draw the bisector AD of ∠A meeting BC in D

Now in triangles ABD and ACD We have AB=AC (Given)

∠BAD=∠CAD (because AD is bisector ofy ∠A

AD=AD (Common side)

Therefore by SAS congruence condition we have

△ABC≅△ACD

⇒∠B=∠C

(Corresponding parts of congruent triangles are equal )

2.

consider Δ ABC and Δ ACD

Since the line segments AB+CD are parallel

to each other and AC is a transversal

∠ ACB = ∠ CAD.

AC = AC (common side)

∠CAB = ∠ ACD.

Thus, by ASA criteria

ΔABC ≅ ΔACD

The corresponding part of the congruent

triangle are congruent

AB = CD + AD = BC

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