a The line of reflection has to be drawn through one of the triangle's vertices. How can we know which one?
B
b Note that m∠ B=m∠ C.
C
c What type of angle pair does ∠ x and the unknown base angle form?
A
aAngles: ∠ B and ∠ C
Explanation: See solution.
B
bMeasure: m∠ B=62^(∘)
Explanation: See solution.
C
c x=109^(∘)
Practice makes perfect
a In any isosceles triangle, if the height is drawn from the vertex angle and not from one of the base angles, it will cut the base 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.
b From Part A, we know that the base angles have equal measures. Therefore we can substitute m∠ B for m∠ C into the given equality and then solve for m∠ B.
c From the diagram we can see that the triangle is isosceles, which both base angles have equal measure. Therefore, the other base angle has a measure of 71^(∘).
Examining the diagram, we see that x and one of the base angles form a straight angle pair. This means they are supplementary angles, and therefore their measures have a sum of 180^(∘). With this information we can write and solve an equation for x.
