Question

geometry - kochanowska - f-4,m-4,r-4,t-4,w-4 - kochanowska, jolanta u
topic 3: assessment form a
(image of triangle rst with angle at r: 32°, angle at t: 71°, side st: 4.3 cm)
a. length \\(\overline{rs}=4.3\text{cm}\\)
b. \\(\angle r\cong\angle r\\)
c. \\(m\angle t = 71\\)
d. \\(\overline{st}\cong\overline{ts}\\)
e. length \\(\overline{rt} > \text{length }\overline{rt}\\)

Explanation:

Step1: Analyze Triangle Properties

In a triangle, corresponding parts of congruent triangles (CPCTC) apply if triangles are congruent. Also, angle - side relationships: larger angle opposite longer side. First, find angle at \( S \): \( 180 - 32 - 71=77^{\circ} \).

Step2: Evaluate Option A

\( \overline{ST} = 4.3\mathrm{cm} \). If triangles are congruent, \( \overline{R'S'} \) would correspond to a different side (not \( \overline{ST} \) unless specific congruence). So A is incorrect.

Step3: Evaluate Option B

If triangles are congruent (implied by notation like \( \angle R\cong\angle R' \)), corresponding angles are congruent. This is a property of congruent triangles (CPCTC), so B is correct.

Step4: Evaluate Option C

\( m\angle T = 71^{\circ} \), so \( m\angle T' = 71^{\circ} \) (corresponding angles in congruent triangles), so C is correct.

Step5: Evaluate Option D

\( \overline{ST} \) and \( \overline{T'S'} \): in congruent triangles, \( \overline{ST}\cong\overline{T'S'} \) (corresponding sides), so D is correct.

Step6: Evaluate Option E

In triangle \( RST \), side opposite \( 77^{\circ} \) (angle at \( S \)) is \( RT \), side opposite \( 71^{\circ} \) (angle at \( T \)) is \( RS \), side opposite \( 32^{\circ} \) (angle at \( R \)) is \( ST \). If triangles are congruent, \( RT = R'T' \), so \( \text{length } \overline{RT}=\text{length } \overline{R'T'} \), so E is incorrect.

Answer:

B. \( \angle R\cong\angle R' \), C. \( m\angle T' = 71 \), D. \( \overline{ST}\cong\overline{T'S'} \)