Prove that the base angles of an isosceles triangle are congruent. Be sure to create and name the appropriate geometric figures.

Basically what this question is asking you is that you have to prove the base of the angles of an isosceles triangle is congruent. Isosceles Triangle Theorems. If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

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aachen aachen · Answer 2 · 2019-08-18T08:04:38+02:00

Answer:

Consider the triangle ABC in the attached file.

Given: An isosceles triangle ABC.

To Prove: Base angles of an isosceles triangle are congruent.

Construction: Draw AM perpendicular to BC.

Proof: To prove the base angles of an isosceles triangle are congruent, we first need to prove triangle ABM is congruent to triangle ACM.

In [tex]\Delta {ABM}[/tex] and [tex]\Delta {ACM}[/tex]

[tex]AB=AC\:\:\left [ \because \Delta ABC\: \text {is an isosceles triangle }\right ][/tex]

[tex]\angle \text{AMB}=\angle \text{AMC} \:\left [ \text{Each 90}\right ][/tex]

[tex]\text{AM}=\text{AM}\:\:\left [\text{Common} \right ][/tex]

So, [tex]\Delta \text{ABM}\cong \Delta \text{ACM}[/tex] by AAS criteria.

Therefore, [tex]\angle \text{ABM}=\angle \text{ACM}[/tex] by CPCT.

Hence, the base angles of an isosceles triangle are congruent.