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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 ________.

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Answer:

[tex]\angle B\cong \angle C[/tex]

Step-by-step explanation:

We are given that

[tex]AB\cong AC[/tex]

We have to prove that [tex]\angle B\cong \angle C[/tex]

[tex]AB\cong AC[/tex]

Therefore, AB=AC

Suppose , angle B and angle C are not congruent.

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

If [tex]m\angle B > \angle C[/tex]

Then , [tex]AC > AB[/tex]

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 [tex]m\angle B < m\angle C[/tex]

Then, AC < AB.

It is contradiction because we are given AB=AC.

Therefore, it can be concluded that

[tex]\angle B\cong \angle C[/tex]

Answer:b=c

Step-by-step explanation:

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