Question

question 3 of 10
if $\triangle rstcong\triangle xyz$, which statement must be true?
a. $overline{st}congoverline{xz}$
b. $overline{rs}congoverline{st}$
c. $angle scongangle z$
d. $angle rcongangle x$

Explanation:

Step1: Recall the property of congruent triangles

When two triangles are congruent (\(\triangle RST\cong\triangle XYZ\)), their corresponding parts (corresponding angles and corresponding sides) are congruent. The order of the letters in the triangle congruence statement gives the correspondence. That is, \(R\) corresponds to \(X\), \(S\) corresponds to \(Y\), and \(T\) corresponds to \(Z\).

Step2: Analyze each option

• Option A:

In \(\triangle RST\) and \(\triangle XYZ\), \(ST\) corresponds to \(YZ\) (not \(XZ\)). So, \(\overline{ST}
ot\cong\overline{XZ}\).

• Option B:

\(\overline{RS}\) and \(\overline{ST}\) are sides of \(\triangle RST\). There is no information given that these two sides are congruent. Congruence of triangles only guarantees correspondence between triangles, not within a single triangle unless specified.

• Option C:

\(\angle S\) corresponds to \(\angle Y\) (not \(\angle Z\)). So, \(\angle S
ot\cong\angle Z\).

• Option D:

Since \(R\) corresponds to \(X\) in the congruent triangles \(\triangle RST\cong\triangle XYZ\), by the property of congruent triangles (corresponding parts of congruent triangles are congruent - CPCTC), \(\angle R\cong\angle X\).

Answer:

D. \(\angle R\cong\angle X\)