1) A and C are similar. Reason: AA (Angle-Angle) similarity criterion. Both have angles of 100° and 30° (Triangle A) and 100° and 50° (Triangle C). Since the sum of angles in a triangle is 180°, the third angle in Triangle A is 50° and in Triangle C is 30°. Therefore, both triangles have the same set of angles: 100°, 50°, and 30°.
2) A and C are similar. Reason: AA (Angle-Angle) similarity criterion. Triangle A has angles of 90° and 55°, so its third angle is 35°. Triangle C has angles of 55° and 35°, so its third angle is 90°. Both triangles have angles of 90°, 55°, and 35°.
3) A and C are similar. Reason: SSS (Side-Side-Side) similarity criterion. The side lengths of Triangle A are 6, 8, and 10. The side lengths of Triangle C are 4, 5, and 6. Comparing corresponding sides: 6/4 = 1.5, 8/5 = 1.6, 10/6 ≈ 1.67. These ratios are not equal, so A and C are not similar by SSS. Let's check A and B: 6/9 = 2/3, 8/12 = 2/3, 10/15 = 2/3. All ratios are equal, so A and B are similar by SSS.
Correction for 3): A and B are similar. Reason: SSS (Side-Side-Side) similarity criterion. The ratios of corresponding sides are 6/9 = 8/12 = 10/15 = 2/3.
4) A and C are similar. Reason: SAS (Side-Angle-Side) similarity criterion. Triangle A has sides 6 and 11 with an included angle of 25°. Triangle C has sides 10.2 and 18.7 with an included angle of 25°. The ratio of the sides is 10.2/6 = 1.7 and 18.7/11 = 1.7. Since the included angles are equal and the adjacent sides are in proportion, the triangles are similar by SAS.
Parent Tip: Review the logic above to help your child master the concept of triangles math worksheet.
