Similar Triangles (A) Worksheet | PDF Printable Geometry Worksheet - Free Printable

Final Answer:
1) A and C — AA similarity (both have 30° and 100° angles)
2) A and C — AA similarity (both have 55° and 90° angles)
3) A and C — SSS similarity (side ratios 6:4 = 8:5? Wait—check again: A: 6, 8, 10; C: 4, 5, 6 → not proportional. Actually A and B: A = 6-8-10, B = 9-12-15 → all sides ×1.5 → SSS similarity. C = 4-5-6 → not proportional to either. So A and B are similar.)
Wait—recompute carefully:

Triangle A: sides 6, 8, 10
Triangle B: sides 9, 12, 15 → divide by 3: 3, 4, 5 → same ratio as A (6:8:10 = 3:4:5) → yes, A and B similar by SSS.
Triangle C: 4, 5, 6 → ratios 4:5:6 ≠ 3:4:5 → not similar.

So 3) A and B — SSS similarity

4) Triangle A: sides 6, 11, and included angle 25°
Triangle C: sides 10.2, 18.7, angle 25°
Check ratio: 10.2 / 6 = 1.7; 18.7 / 11 = 1.7 → same scale factor, and included angle equal → SAS similarity.
Triangle B has 30°, not 25°, so not matching.

Thus:
1) A and C
2) A and C
3) A and B
4) A and C

But wait—question 1: Triangle A angles: 30°, 100°, so third = 50°
Triangle C: 100°, 50°, so third = 30° → yes, same angles → A and C similar.
Triangle B: 40°, 100°, so third = 40° → not matching.

Question 2:
A: right angle (90°), 55°, so third = 35°
B: right angle, 45°, third = 45°
C: 55°, 35°, so third = 90° → yes, A and C both have 55°, 35°, 90° → A and C similar.

Question 3:
A: 6, 8, 10 → ratios 3:4:5
B: 9, 12, 15 → divide by 3 → 3:4:5 → same → A and B similar
C: 4, 5, 6 → 4:5:6 ≠ 3:4:5 → not similar.

Question 4:
A: sides 6 and 11 with included angle 25°
C: sides 10.2 and 18.7 with included angle 25°
10.2 ÷ 6 = 1.7
18.7 ÷ 11 = 1.7 → exact match → SAS similarity
B has 30° angle, not 25°, so no.

Final correct pairs:
1) A and C
2) A and C
3) A and B
4) A and C

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Explanation:
- For triangles to be similar, their angles must match (AA rule), or side ratios must be equal (SSS), or two sides and the included angle must match (SAS).
- In #1: Triangle A has angles 30°, 100°, so the third is 50°. Triangle C has 100° and 50°, so third is 30° — same three angles → similar.
- In #2: Triangle A has a right angle (90°) and 55°, so third is 35°. Triangle C has 55° and 35°, so third is 90° — same angles → similar.
- In #3: Triangle A sides 6-8-10 simplify to 3-4-5. Triangle B sides 9-12-15 also simplify to 3-4-5 → all sides in same ratio → similar. Triangle C (4-5-6) doesn’t match.
- In #4: Triangle A has two sides 6 and 11 with angle 25° between them. Triangle C has sides 10.2 and 18.7 with same 25° angle. 10.2/6 = 1.7 and 18.7/11 = 1.7 → same scale, same included angle → similar by SAS.