1. For triangles ABC and DEF:
- Since angle A = angle D, angle B = angle E, and angle C = angle F, the triangles are similar by AAA similarity.
- The ratio of corresponding sides is AB/DE = 20/10 = 2.
- Therefore, BC/EF = 2 → 25/EF = 2 → EF = 12.5 cm.
- Similarly, AC/DF = 2 → 15/DF = 2 → DF = 7.5 cm.
2. For triangles GHI and JKL:
- Given angle G = angle J, angle H = angle K, angle I = angle L, so triangles are similar by AAA.
- Ratio of corresponding sides: GH/JK = 18/9 = 2.
- Thus, HI/KL = 2 → 24/KL = 2 → KL = 12 cm.
- Similarly, GI/JL = 2 → 15/JL = 2 → JL = 7.5 cm.
3. For triangles MNO and PQR:
- Angles correspond: angle M = angle P, angle N = angle Q, angle O = angle R → similar by AAA.
- Ratio MN/PQ = 12/6 = 2.
- So, NO/QR = 2 → 16/QR = 2 → QR = 8 cm.
- MO/PR = 2 → 10/PR = 2 → PR = 5 cm.
4. For triangles STU and VWX:
- Given angle S = angle V, angle T = angle W, angle U = angle X → similar by AAA.
- Ratio ST/VW = 14/7 = 2.
- Thus, TU/WX = 2 → 21/WX = 2 → WX = 10.5 cm.
- SU/VX = 2 → 18/VX = 2 → VX = 9 cm.
5. For triangles YZA and BCD:
- Angles correspond: angle Y = angle B, angle Z = angle C, angle A = angle D → similar by AAA.
- Ratio YZ/BC = 22/11 = 2.
- So, ZA/CD = 2 → 28/CD = 2 → CD = 14 cm.
- YA/BD = 2 → 20/BD = 2 → BD = 10 cm.
6. For triangles EFG and HIJ:
- Given angle E = angle H, angle F = angle I, angle G = angle J → similar by AAA.
- Ratio EF/HI = 16/8 = 2.
- Thus, FG/IJ = 2 → 20/IJ = 2 → IJ = 10 cm.
- EG/HJ = 2 → 12/HJ = 2 → HJ = 6 cm.
7. For triangles KLM and NOP:
- Angles correspond: angle K = angle N, angle L = angle O, angle M = angle P → similar by AAA.
- Ratio KL/NO = 10/5 = 2.
- So, LM/OP = 2 → 15/OP = 2 → OP = 7.5 cm.
- KM/NP = 2 → 12/NP = 2 → NP = 6 cm.
8. For triangles QRS and TUV:
- Given angle Q = angle T, angle R = angle U, angle S = angle V → similar by AAA.
- Ratio QR/TU = 18/9 = 2.
- Thus, RS/UV = 2 → 24/UV = 2 → UV = 12 cm.
- QS/TV = 2 → 15/TV = 2 → TV = 7.5 cm.
9. For triangles WXY and ZAB:
- Angles correspond: angle W = angle Z, angle X = angle A, angle Y = angle B → similar by AAA.
- Ratio WX/ZA = 20/10 = 2.
- So, XY/AB = 2 → 25/AB = 2 → AB = 12.5 cm.
- WY/ZB = 2 → 15/ZB = 2 → ZB = 7.5 cm.
10. For triangles CDE and FGH:
- Given angle C = angle F, angle D = angle G, angle E = angle H → similar by AAA.
- Ratio CD/FG = 12/6 = 2.
- Thus, DE/GH = 2 → 18/GH = 2 → GH = 9 cm.
- CE/FH = 2 → 14/FH = 2 → FH = 7 cm.
Parent Tip: Review the logic above to help your child master the concept of similar triangle worksheet.
