Question

question 5. given that the two triangles shown are congruent, explain one way to verify that the corresponding angles of the two triangles are congruent. a. reflect across the vertical axis and rotate 180° b. reflect across the horizontal axis c. reflect across the vertical axis d. reflect across the horizontal axis and rotate 180°

Explanation:

Step1: Analyze each option

• Option A: Reflecting across the vertical axis and rotating \(180^{\circ}\) is an unnecessary complex transformation for these triangles.
• Option B: Reflecting across the horizontal axis does not map one triangle onto the other as per their orientation.
• Option C: Reflecting across the vertical axis (the purple line in the figure) will map \(\triangle ABC\) onto \(\triangle A'B'C'\) such that corresponding vertices (and thus corresponding angles) coincide.
• Option D: Reflecting across the horizontal axis and rotating \(180^{\circ}\) is an over - complicated and incorrect transformation for showing the congruence of corresponding angles.

Answer:

C. reflect across the vertical axis