1. ΔRST ~ ΔRFG or ΔFRG
By AA Similarity (both share ∠R, and both have a right angle)
Little to Big Ratio: 5/8
2. ΔXYZ ~ ΔKJP or ΔPKJ
By SSS Similarity (sides are proportional: 2.4/6 = 7/17.5 = 10/25 = 0.4)
Little to Big Ratio: 2/5
3. ΔMNO ~ ΔHIJ or ΔJIH
By SAS Similarity (∠N ≅ ∠I, and sides adjacent to these angles are proportional: 20/40 = 30/60 = 0.5)
Little to Big Ratio: 1/2
4. ΔDEF ~ ΔACB or ΔBCA
By SAS Similarity (∠F ≅ ∠C (right angles), and sides adjacent to these angles are proportional: 5/10 = 6/12 = 0.5)
Little to Big Ratio: 1/2
5. ΔDEF ~ ΔABC or ΔBCA
By SSS Similarity (sides are proportional: 9/27 = 21/63 = 25/75 = 1/3)
Little to Big Ratio: 1/3
6. ΔDEF ~ ΔABC or ΔBCA
By AA Similarity (∠E ≅ ∠B (both 60°), ∠F ≅ ∠C (both 30°))
Little to Big Ratio: 1/2
7. ΔRST ~ ΔRTL or ΔLTR
By AA Similarity (∠R ≅ ∠R, ∠S ≅ ∠T (both 50°))
Little to Big Ratio: 4/7
8. ΔABC ~ ΔADE or ΔEDA
By AA Similarity (∠A ≅ ∠A, ∠B ≅ ∠D (corresponding angles if BC || DE))
Little to Big Ratio: 2/5
9. ΔABC ~ ΔUVW or ΔWVU
By AA Similarity (∠A ≅ ∠U, ∠B ≅ ∠V, ∠C ≅ ∠W)
Little to Big Ratio: 3/5
10. Alicia is correct.
Reasoning: In similar triangles, corresponding sides are proportional. The correct proportion sets the ratio of side 'l' in the first triangle to its corresponding side 'k' in the second triangle equal to the ratio of side 's' in the first triangle to its corresponding side 'm' in the second triangle: l/k = s/m. Cross-multiplying gives lm = ks. Jason's equation, rs = km, incorrectly pairs non-corresponding sides.
Parent Tip: Review the logic above to help your child master the concept of triangle similarity theorems worksheet.
