IXL - Congruency in isosceles and equilateral triangles (Geometry practice)

What is the value of

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What is the value of

The Isosceles Triangle Theorem states that two sides of a triangle are congruent if and only if the angles opposite those sides are congruent.

Angles marked with the same number of arcs are congruent.

Look at the diagram.

∠

and

∠

are marked with one arc each. So, they are congruent.

By the Isosceles Triangle Theorem, the sides opposite

∠

and

∠

must also be congruent.

The side opposite

∠

and the side opposite

∠

So,

and

have the same length. From the diagram you can see that the length of

is 6 and the length of

For these to be the same,

must equal 6.

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