Congruent Triangles
Triangles ABC and A′B′C′ in Fig. 9.23 are congruent. Determine
a) the length of side A′C′. b) the length of side \overline{AB}.
c) m∡C^′A^′B^′. d) m∡ACB.
e) m∡ABC.
Because ΔABC is congruent to ΔA′B′C′, we know that the corresponding side lengths are equal and corresponding angle measures are equal.
a) A′C′ = AC = 13 b) AB = A′B′ = 10.6
c) m∡C^′A^′B^′ = m∡CAB = 60° d) m∡ACB = m∡A^′C^′B^′ = 50°
e) The sum of the angles of a triangle is 180°. Since m∡BAC = 60° and m∡ACB = 50°, m∡ABC = 180° – 60° – 50° = 70°.