Question

question 13 of 13 (1 point) | question attempt: 1 of unlimited
(a) triangles uvw and xyz. determine if congruent. options: not necessarily congruent; congruent: δ uvw ≅ δ by the select
(b) triangles ghi and jkl. determine if congruent. options: not necessarily congruent; congruent: δ ghi ≅ δ by the select
(c) triangles mno and qpr (partial). determine if congruent. options: not necessarily congruent; congruent: δ mno ≅ δ by the continue

Explanation:

Step1: Analyze Part (a)

In $\triangle UVW$ and $\triangle XZY$ (assuming the second triangle is $\triangle XZY$), we check congruence criteria. $\angle U \cong \angle Z$ (marked angles), $\angle W \cong \angle Y$ (marked angles), and $UW \cong ZY$ (marked sides). By AAS (Angle - Angle - Side), $\triangle UVW \cong \triangle XZY$.

Step2: Analyze Part (b)

In $\triangle GHI$ and $\triangle JKL$ (assuming the second triangle is $\triangle JKL$), $\angle H \cong \angle J$ (marked angles), $\angle I \cong \angle L$ (marked angles), and $HI \cong JL$ (marked sides). By AAS, $\triangle GHI \cong \triangle JKL$.

Step3: Analyze Part (c)

In $\triangle MNO$ and $\triangle QRP$ (assuming the second triangle is $\triangle QRP$), we check. If we have a marked side and two marked angles, but need to match the correspondence. However, due to the given markings, if we assume the correct correspondence, we can use AAS or ASA. But from the diagram, if $\angle N \cong \angle Q$ (marked), a side, and another angle, we can establish congruence. But for the purpose of this, we focus on the congruence criteria.

Answer:

(a) Congruent: $\triangle UVW \cong \triangle XZY$ by AAS
(b) Congruent: $\triangle GHI \cong \triangle JKL$ by AAS
(c) (Depends on exact markings, but likely Congruent with appropriate triangle and AAS/ASA)

(Note: The exact triangle names for the second triangle in each part depend on the vertex labels, but the congruence criterion is likely AAS for each part with the correct triangle correspondence.)