Concept. ___. BCA is opposite BA and A is opposite BC , so BCA A. ___. Congruent Segments and Angles. A. Name two unmarked congruent angles. Answer: BCA and A. Example 1. ___. BC is opposite D and BD is opposite BCD , so BC BD. ___. ___. ___. ___.
Since QP = QR, QP QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so mP = mR . Use the Triangle Sum Theorem to write and solve an equation to find mR.
Find Missing Measures
A. Find mR.
Triangle Sum Theorem
mQ = 60, mP = mR
Subtract 60 from each side.
Answer:mR = 60
Divide each side by 2.Example 2
mDFE = 60 Definition of equilateral triangle
4x – 8 = 60 Substitution
4x = 68 Add 8 to each side.
x = 17 Divide each side by 4.
The triangle is equilateral, so all the sides are congruent, and the lengths of all of the sides are equal.
DF = FE Definition of equilateral triangle
6y + 3 = 8y – 5 Substitution
3 = 2y – 5 Subtract 6y from each side.
8 = 2y Add 5 to each side.Example 3
Given:HEXAGO is a regular polygon. ΔONG is equilateral, N is the midpoint of GE, and EX || OG.
Prove:ΔENX is equilateral.
Apply Triangle Congruence
NATURE Many geometric figures can be found in nature. Some honeycombs are shaped like a regular hexagon. That is, each of the six sides and interior angle measures are the same.Example 4