Question

decide whether the triangles are similar. if they are, write a similarity statement and state the reason justifying the similarity. if necessary, you may learn what the markings on a figure indicate.1. △xyz ~ □ by the○ not similar or not necessarily similar○ similar:2. △abc ~ □ by the○ not similar or not necessarily similar○ similar:3. △jkl ~ □ by the○ not similar or not necessarily similar○ similar:

Explanation:

Step1: Analyze △XYZ and △NMY

∠XYZ = ∠NMY (vertical angles, equal). ∠XZY = ∠MNY (right angles, equal). By AA (Angle-Angle) Similarity, the triangles are similar.

Step2: Analyze △ABC and △EDF

Calculate side ratios: $\frac{AB}{ED}=\frac{6}{4}=1.5$, $\frac{BC}{DF}=\frac{7}{5}=1.4$, $\frac{AC}{EF}=\frac{8}{6}\approx1.33$. Ratios are not equal, so no similarity via SSS. No angle info for AA/SAS, so not necessarily similar.

Step3: Analyze △JKL and △HIG

Find missing angle in △JKL: $180^\circ - 30^\circ - 20^\circ = 130^\circ$. In △HIG, angles are $50^\circ, 110^\circ, 20^\circ$. Only one matching angle, so no AA similarity. No side ratio info, so not necessarily similar.

Answer:

1. $\triangle XYZ \sim \triangle NMY$ by the AA (Angle-Angle) Similarity Criterion
2. Not similar or not necessarily similar
3. Not similar or not necessarily similar