a What do you call a triangle with two congruent sides?
B
b What can you say about the base angles of an isosceles triangle?
A
a Isosceles triangle
B
b 70^(∘) Explantion: See solution.
Practice makes perfect
a From the information in the exercise, we know that the triangle has two sides that are both 144 feet. Since two sides are congruent, this is an isosceles triangle.
b According to the Base Angles Theorem, if two sides of a triangle are congruent, then the angles opposite them are congruent. Let's add this information, including the measure of ∠ 3, to the diagram.
According to the Triangle Sum Theorem, the sum of the measures of the interior angles of a triangle is 180^(∘). This allows us to write the following equation:
m∠ 1+m∠ 2+40^(∘)=180^(∘).
Since m∠ 1=m∠ 2, we can substitute m∠ 1 with m∠ 2 and solve for the measure of the base angles.
