Congruency of Triangles Practice

Question

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4 of 54 of 5 Items

Question
Use the image to answer the question.

A coordinate plane showing 4 quadrants has two triangles plotted on it. Triangle upper A upper B upper C is plotted in quadrant 2, and triangle upper A prime upper B prime upper C prime is plotted in quadrant 4.

If △ABC≅△A′B′C′
, which option denotes three pairs of congruent corresponding parts?

Option #1: ∠A≅∠A′
, AB¯¯¯¯¯¯¯¯≅A′B′¯¯¯¯¯¯¯¯¯¯
, and CB¯¯¯¯¯¯¯¯≅A′B′¯¯¯¯¯¯¯¯¯¯

Option #2: CB¯¯¯¯¯¯¯¯≅C′B′¯¯¯¯¯¯¯¯¯¯¯
, AC¯¯¯¯¯¯¯¯≅A′C′¯¯¯¯¯¯¯¯¯¯¯
, ∠C′≅∠C

Option #3. BC¯¯¯¯¯¯¯¯≅B′C′¯¯¯¯¯¯¯¯¯¯¯
, ∠B≅∠C′
, ∠B′≅∠C

(1 point)
Option #
denotes the full set of correct corresponding parts.

Answer 1

To determine which option denotes three pairs of congruent corresponding parts for the triangles \( \triangle ABC \) and \( \triangle A'B'C' \) where \( \triangle ABC \cong \triangle A'B'C' \), we need to recall that corresponding parts of congruent triangles are equal, which includes corresponding angles and sides.

Let's analyze each option:

Option #1:

• \( \angle A \cong \angle A' \) (1 pair of angles)
• \( AB \cong A'B' \) (1 pair of sides)
• \( CB \cong A'B' \) (here it seems there might be a mistake, as it should match with \( AC \) or \( BC \), but it's given as \( A'B' \), which doesn't correspond to the other triangle's sides accurately)

This option does not have three correct pairs.

Option #2:

• \( CB \cong C'B' \) (1 pair of sides)
• \( AC \cong A'C' \) (1 pair of sides)
• \( \angle C' \cong \angle C \) (1 pair of angles)

This option has three correct pairs.

Option #3:

• \( BC \cong B'C' \) (1 pair of sides)
• \( \angle B \cong \angle C' \) (this helps check correspondence, but should verify angles)
• \( \angle B' \cong \angle C \) (this also suggests consideration, but angles between two should maintain correspondence per triangles)

This option has issues as we don't know the angles' corresponding values based on their placement.

Based on this analysis, Option #2 has three valid pairs of corresponding congruent parts based on the congruency of the triangles.

Answer: Option #2.