b What type of angle pair does ∠ y and the unknown base angle form?
A
a x=45^(∘)
What Kind of Triangle Is △ ABC? Isosceles
B
b y=109^(∘)
What Kind of Triangle? Isosceles
Practice makes perfect
a In any isosceles triangle, if the height is drawn from the vertex angle and not from any of the base angles, it will cut the base side into two equal halves and therefore create a pair of identical right triangles.
Since the triangles are identical we are able to fold one of them over the other, using the dotted line as a crease.
When folding we see that ∠ B and ∠ C line up. This means ∠ B and ∠ C must have equal measures.
According to the Triangle Angle Sum Theorem the sum of a triangle's angles equals 180^(∘). With this information, we can set up an equation and solve for x.
b From the diagram we see that the triangle is isosceles, which means its second base angle is 71^(∘) as well.
Examining the diagram, we see that y and the second base angle form a linear pair. This means they are supplementary angles, and therefore sum to 180^(∘). With this information we can write and solve an equation for y.
