Question

determine if the triangles are similar by angle-angle similarity
1)
2)
3)
4)
5)
6)

Explanation:

Step1: Analyze Problem 1

Triangles CDE and FGE: ∠D=∠G=90°, ∠CED=∠FEG (vertical angles). AA similarity holds.

Step2: Analyze Problem 2

Triangles LQP and LMN: ∠L=common angle, QP∥MN (arrows), so ∠LQP=∠LMN. AA similarity holds.

Step3: Analyze Problem 3

Triangle SYE: ∠Y=90°, ∠E=39°, so ∠S=51°. Triangle HWC: ∠C=90°, ∠H=51°, so ∠W=39°. ∠Y=∠C=90°, ∠S=∠H=51°. AA similarity holds.

Step4: Analyze Problem 4

Triangle ABD: ∠A=68°, ∠D=54°, so ∠B=58°. Triangle EFG: ∠F=68°, ∠G=63°, so ∠E=49°. No two equal angles. AA similarity fails.

Step5: Analyze Problem 5

Triangle LMN: ∠L=25°, ∠N=67°, so ∠M=88°. Triangle LBC: ∠L=25°, ∠BCL=91°, so ∠LBC=64°. No two equal angles. AA similarity fails.

Step6: Analyze Problem 6

Triangles PXZ and QYZ: ∠PXZ=∠QYZ (vertical angles), ∠P=∠Q (marked right angles). AA similarity holds.

Answer:

1. Similar
2. Similar
3. Similar
4. Not similar
5. Not similar
6. Similar