Question

name two pairs of congruent angles in the figure. justify the answer
select all that apply
a. ∠wit and ∠sir according to the congruent complements theorem
b. ∠sir and ∠tis according to the right angles congruent theorem
c. ∠wis and ∠tir according to the right angles congruent theorem
d. ∠wit and ∠tis according to the congruent complements theorem
e. ∠tir and ∠wit according to the linear pair theorem

Explanation:

• For option A:
• The Congruent Complements Theorem states that if two angles are complementary to the same angle, then they are congruent.
• \(\angle WIT+\angle TIS = 90^{\circ}\) (since \(\angle WIS = 90^{\circ}\)) and \(\angle SIR+\angle TIS=90^{\circ}\) (since \(\angle TIR = 90^{\circ}\)). So \(\angle WIT\) and \(\angle SIR\) are complementary to \(\angle TIS\), and by the Congruent Complements Theorem, \(\angle WIT\cong\angle SIR\).
• For option C:
• The Right Angles Congruent Theorem states that all right angles are congruent.
• \(\angle WIS = 90^{\circ}\) and \(\angle TIR=90^{\circ}\), so \(\angle WIS\cong\angle TIR\) by the Right Angles Congruent Theorem.

Answer:

A. \(\angle WIT\) and \(\angle SIR\) according to the Congruent Complements Theorem; C. \(\angle WIS\) and \(\angle TIR\) according to the Right Angles Congruent Theorem.