Question

1. triangle xyz has sides xy = 3, yz = 5, and xz = 6. which set of side lengths ensures triangle abc is congruent to triangle xyz by sss? a. ab = 6, bc = 3, ac = 5 b. ab = 5, bc = 6, ac = 4 c. ab = 3, bc = 6, ac = 5 d. ab = 3, bc = 5, ac = 6 14. if two triangles have ab = de, ac = df, and ∠bac = ∠edf, which congruence rule applies? a. aas b. sss c. asa d. sas 15. given that △jkl ≅ △mno by asa, which of the following statements is true? a. ∠j = ∠o b. jk = mo c. ∠k = ∠n d. kl = mn

Explanation:

Step1: Recall SSS congruence rule

For two triangles to be congruent by SSS (Side - Side - Side), their corresponding sides must be equal. In $\triangle XYZ$, $XY = 3$, $YZ=5$, $XZ = 6$. For $\triangle ABC$ to be congruent to $\triangle XYZ$ by SSS, $AB=XY = 3$, $BC = YZ=5$, $AC=XZ = 6$. So the answer to question 13 is d.

Step2: Recall congruence rules

In two triangles, if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, the congruence rule is SAS (Side - Angle - Side). Given $AB = DE$, $AC = DF$, and $\angle BAC=\angle EDF$, the congruence rule is SAS. So the answer to question 14 is d.

Step3: Recall ASA congruence implications

If $\triangle JKL\cong\triangle MNO$ by ASA (Angle - Side - Angle), the corresponding angles and sides are equal. The angles between the corresponding equal - sides are equal. So if $\triangle JKL\cong\triangle MNO$ by ASA, $\angle K=\angle N$. So the answer to question 15 is c.

Answer:

1. d. $AB = 3, BC = 5, AC = 6$
2. d. SAS
3. c. $\angle K=\angle N$