Question

Since it is given that AB ≅ AC, it must also be true that AB = AC. Assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other. If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem. For the same reason, if m∠B < m∠C, then AC < AB. This is a contradiction to what is given. Therefore, it can be concluded that ________.

Answer 1

Answer:b=c

Step-by-step explanation:

Answer 2

Answer:

$\angle B\cong \angle C$

Step-by-step explanation:

We are given that

$AB\cong AC$

We have to prove that $\angle B\cong \angle C$

$AB\cong AC$

Therefore, AB=AC

Suppose , angle B and angle C are not congruent.

Then, the measure of one angle is greater than the other.

If $m\angle B > \angle C$

Then , $AC > AB$

By using triangle parts theorem

It states that when an angle is greater than other then opposite side of greater angle is greater than the opposite side of other angle.

If $m\angle B < m\angle C$

Then, AC < AB.

It is contradiction because we are given AB=AC.

Therefore, it can be concluded that

$\angle B\cong \angle C$