Question

name two pairs of congruent angles in the figure. justify the answer.
a. $\angle fjg$ and $\angle jif$ according to the linear pair theorem
b. $\angle jih$ and $\angle fjg$ according to the right angles congruent theorem
c. $\angle jif$ and $\angle hig$ according to the congruent complements theorem
d. $\angle hig$ and $\angle fih$ according to the right angles congruent theorem
e. $\angle jih$ and $\angle hig$ according to the linear pair theorem
f. $\angle jif$ and $\angle fih$ according to the congruent complements theorem
g. $\angle jih$ and $\angle fjg$ according to the congruent complements theorem

Explanation:

Step1: Analyze Angle Relationships

From the figure (assuming right angles at \( \angle JIH \) and \( \angle HIG \) related to \( \angle JIF \) and \( \angle FIH \)), we use the Congruent Complements Theorem. If two angles are complements of the same angle (or congruent angles), they are congruent. \( \angle JIF \) and \( \angle HIG \) are complements of \( \angle FIH \) (or related angles), so by Congruent Complements Theorem, they are congruent. Option C states \( \angle JIF \) and \( \angle HIG \) according to the Congruent Complements Theorem, which matches.

Step2: Eliminate Other Options

• Option A: Linear Pair Theorem is for supplementary angles, not congruent here.
• Option B: Right Angles Congruent Theorem is for right angles, not applicable.
• Option D: Right Angles Congruent Theorem misapplied.
• Option E: Linear Pair Theorem misapplied.
• Option F: Congruent Complements but wrong angles.
• Option G: Congruent Complements but wrong angles.

Answer:

C. \( \angle JIF \) and \( \angle HIG \) according to the Congruent Complements Theorem