This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
a) Step 1: Convert units to be consistent. 7.2 cm = 72 mm 5.8 cm = 58 mm Step 2: Compare the triangles. Both triangles are right-angled. The hypotenuse of the first triangle is 72 mm, and the hypotenuse of the second triangle is 72 mm. One side of the first triangle is 58 mm, and one side of the second triangle is 58 mm. Step 3: Determine congruency. The triangles are congruent because they are right-angled, have equal hypotenuses, and one pair of corresponding sides are equal. This satisfies the RHS (Right angle - Hypotenuse - Side) rule. The triangles are congruent by the RHS rule. b) Step 1: Convert units to be consistent. 7 cm = 70 mm Step 2: Compare the triangles. For the first triangle, two angles are 40^ and 60^, and the included side is 7 cm (70 mm). For the second triangle, two angles are 40^ and 60^, and the included side is 70 mm. Step 3: Determine congruency. Since two angles and the included side are equal in both triangles, they are congruent by the ASA (Angle - Side - Angle) rule. The triangles are congruent by the ASA rule. c) Step 1: Convert units to be consistent. 50 mm = 5 cm 40 mm = 4 cm Step 2: Compare the triangles. The sides of the first triangle are 4 cm, 6 cm, and 5 cm. The sides of the second triangle are 6 cm, 5 cm, and 4 cm. Step 3: Determine congruency. All three corresponding sides of the triangles are equal. This satisfies the SSS (Side - Side - Side) rule. The triangles are congruent by the SSS rule. Send me the next one 📸