- 1a) Similar. ΔPQR ~ ΔXYZ (SSS similarity: 8/4 = 9/6 = 12/8 = 2)
- 1b) Similar. ΔEFG ~ ΔGHI (SSS similarity: 8/16 = 9/18 = 12/24 = 1/2)
- 2) Not similar. ΔABC has angles 28°, 90°, 62°; ΔPQR has angles 62°, 90°, 28°. The angles are the same but the correspondence is not preserved in the naming (e.g., ∠A=28° vs ∠Q=90°).
- 3) Similar. ΔABC ~ ΔDEC (AA similarity: ∠A=∠D=40°, ∠B=∠E=60°, and vertical angles at C are equal)
- 4) Not similar. Side ratios: 30/45 ≠ 32/36 ≠ 24/48 (2/3 ≠ 8/9 ≠ 1/2)
- 5) Not similar. ΔABC has angles 90°, 60°, 30°; ΔXYZ has angles 90°, 30°, 60°. The triangles are similar by AA, but the vertex correspondence in the names does not match the angle correspondence (e.g., ∠A=90° vs ∠X=30°). If we consider the triangles themselves, they are similar, but the statement ΔABC ~ ΔXYZ is incorrect based on naming.
- 6) Similar. ΔMFG ~ ΔMKL (AA similarity: ∠M common, ∠MFG = ∠MKL = 54°, so third angles are also equal)
- 7) Similar. ΔEFG ~ ΔKLM (AA similarity: ∠E=∠K=40°, ∠F=∠L=100°, so third angles are also equal)
Parent Tip: Review the logic above to help your child master the concept of triangle similarity proofs worksheet.
