Question

triangles ghi and jkl are congruent by sas with gh = 7 cm, hi = 9 cm, and ∠ghi = 65 degrees. what is the measure of ∠jkl? a. 55 degrees b. 65 degrees c. 75 degrees d. 85 degrees in proving congruence, which postulate involves using two angles and the included side? a. hl b. asa c. sas d. sss triangles abc and def are congruent by sss with ab = 9 cm, bc = 11 cm, and ca = 13 cm. what is the length of de? a. 9 cm b. 13 cm c. 15 cm d. 11 cm

Explanation:

Step1: Recall congruent - triangle property

Congruent triangles have equal corresponding parts. Since $\triangle GHI\cong\triangle JKL$ by SAS and $\angle GHI$ and $\angle JKL$ are corresponding angles, they are equal.
So, $\angle JKL=\angle GHI = 65^{\circ}$.

Step2: Recall congruence postulate definitions

The ASA (Angle - Side - Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step3: Recall SSS congruence property

If $\triangle ABC\cong\triangle DEF$ by SSS, then corresponding sides are equal. $AB$ and $DE$ are corresponding sides. Given $AB = 9$ cm, so $DE=9$ cm.

Answer:

1. B. 65 degrees
2. B. ASA
3. A. 9 cm