Question

In △ ABC, ∠C = 57° and ∠A = 103°. Side CB= 6.5 cm. Draw △ A′B′C′ under the same condition as △ ABC. Leave all construction marks as evidence of your work, and label all side and angle measurements(use text box). What can you conclude about △ ABC and △ A′B′C′? Justify your response.

Answer 1

ΔA'B'C' is congruent to ΔABC

Explanation:

See attached for the construction of ΔA'B'C'. (The vertices are labeled ABC.)

We computed angle B to be ...

∠B = 180° -∠A -∠C

∠B = 180° -103° -57° = 20°

We constructed segment BC of length 6.5. Then we constructed angles of 20° and 57° from B and C, respectively. The location where the rays from those angles cross is point A', and the angle there is 103°, as required.

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ΔA'B'C' is congruent to ΔABC by the ASA congruence postulate.