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Describing Triangles

Describing Triangles 1.11 - Solution

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a

Consider the given diagram.

We see that two sides in a triangle are congruent. According to the base angles theorem the angles opposite these sides are congruent. By the theorem we know that Therefore, these two angles have the same measure.

Next, we know by the interior angles theorem that the sum of the measures of the interior angles of a triangle equals

Applying the theorem, we can write an equation in terms of Let's solve the equation for
Solve for
b

Consider the given diagram. Note that and therefore is an isosceles triangle. The triangle's vertex angle, is bisected by

For the triangle we can apply the base angles theorem. Thus, and they must have the same measure.

Next, we apply use the interior angles theorem on