Question

name two pairs of congruent angles in the figure. justify the answer. select all that apply. a. ∠xiz and ∠yiw according to the congruent complements theorem b. ∠yiw and ∠xiy according to the linear pair theorem c. ∠ziw and ∠yiz according to the right angles congruent theorem d. ∠xiy and ∠yiz according to the congruent complements theorem e. ∠xiz and ∠ziw according to the linear pair theorem f. ∠xiz and ∠yiw according to the right angles congruent theorem g. ∠xiy and ∠ziw according to the congruent complements theorem

Explanation:

• Congruent Complements Theorem: If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent.
• Linear - Pair Theorem: If two angles form a linear pair, they are supplementary (sum to 180°), but not necessarily congruent.
• Right - Angles Congruent Theorem: All right angles are congruent.
• Analyze option A: ∠XIZ and ∠YIW are complements of ∠XIY and ∠YIZ respectively. By the Congruent Complements Theorem, they can be congruent.
• Analyze option B: ∠YIW and ∠XIY form a linear - pair. By the Linear - Pair Theorem, they are supplementary, not congruent.
• Analyze option C: ∠ZIW and ∠YIZ are not right - angles in the given context.
• Analyze option D: ∠XIY and ∠YIZ are adjacent angles, not related by the Congruent Complements Theorem.
• Analyze option E: ∠XIZ and ∠ZIW form a linear - pair. By the Linear - Pair Theorem, they are supplementary, not congruent.
• Analyze option F: ∠XIZ and ∠YIW are not right - angles in the given context.
• Analyze option G: ∠XIY and ∠ZIW are complements of ∠YIZ and ∠XIY respectively. By the Congruent Complements Theorem, they can be congruent.

Answer:

A. ∠XIZ and ∠YIW according to the Congruent Complements Theorem
G. ∠XIY and ∠ZIW according to the Congruent Complements Theorem