Math / Geometry

QuestionGiven that $\triangle C A R \cong \triangle P E T$ , which of the following must be true? $\angle C \cong \angle P$ $\overline{R A} \cong \overline{T P}$ Two of these $\overline{C R} \cong \overline{E T}$

Studdy Solution

STEP 1

1. The triangles $\triangle C A R$ and $\triangle P E T$ are congruent.
2. Congruent triangles have corresponding sides and angles that are equal.

STEP 2

1. Identify corresponding parts of congruent triangles.
2. Determine which statements must be true based on the congruence.

STEP 3

Identify the corresponding parts of the congruent triangles $\triangle C A R$ and $\triangle P E T$ . The order of the letters in the triangle names indicates the correspondence: - $C$ corresponds to $P$ - $A$ corresponds to $E$ - $R$ corresponds to $T$

STEP 4

Determine which statements must be true based on the congruence of the triangles. Since the triangles are congruent, corresponding angles and sides are equal: - $\angle C \cong \angle P$ is true because $C$ corresponds to $P$ . - $\overline{R A} \cong \overline{T P}$ is false because $R A$ corresponds to $T E$ . - $\overline{C R} \cong \overline{E T}$ is true because $C R$ corresponds to $P T$ .
Since two statements are true ( $\angle C \cong \angle P$ and $\overline{C R} \cong \overline{E T}$ ), the correct answer is:
"Two of these"

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