In triangle $ ABC $, $\overline{AB} = 6 ext{ m}$, $\overline{BC} = 8 ext{ m}$, and $\overline{AC} = 10 ext{

Question

In triangle $ ABC $, $\overline{AB} = 6	ext{ m}$, $\overline{BC} = 8	ext{ m}$, and $\overline{AC} = 10	ext{ m}$. In triangle $ PRQ $, $\overline{PR} = 8	ext{ m}$, $\overline{PQ} = 10	ext{ m}$, and $\overline{RQ} = 6	ext{ m}$. Which of the following is a correct order of congruency?

Examoogle · Accepted Answer

The correct answer is $\Delta BCA \cong \Delta RPQ$. Match corresponding sides by length: AB = 6, BC = 8, AC = 10 corresponds to RQ = 6, PR = 8, PQ = 10. Thus, vertex A corresponds to R, B to Q, and C to P.

Step-by-Step Solution & Concepts:
Shortcut Trick: Match corresponding sides by length: AB = 6, BC = 8, AC = 10 corresponds to RQ = 6, PR = 8, PQ = 10. Thus, vertex A corresponds to R, B to Q, and C to P.

Formula Used: $$\Delta ABC \cong \Delta PRQ$$

Given: Triangle ABC with side lengths AB = 6 m, BC = 8 m, AC = 10 m; Triangle PRQ with side lengths PR = 8 m, PQ = 10 m, RQ = 6 m

Steps: Analyze Given Side Lengths of Triangle ABC: We are given the lengths of the sides of triangle ABC: $AB = 6	ext{ m}$, $BC = 8	ext{ m}$, and $AC = 10	ext{ m}$.. Analyze Given Side Lengths of Triangle PRQ: For triangle PRQ, the given side lengths are: $PR = 8	ext{ m}$, $PQ = 10	ext{ m}$, and $RQ = 6	ext{ m}$.. Determine Vertex Correspondence: Matching the sides by their lengths: - $AB = 6	ext{ m}$ corresponds to $RQ = 6	ext{ m}$ $ightarrow A$ corresponds to $

Examoogle · Answer

Option A: $\Delta BCA $\cong$ $	riangle RP$Q$

Examoogle · Answer

Option B: $\Delta ABC $\cong$ $	riangle RP$Q$

Examoogle · Answer

Option C: $\Delta BAC $\cong$ $	riangle RP$Q$

Examoogle · Answer

Option D: $\Delta CBA $\cong$ $	riangle RP$Q$

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