Triangles

Answer

Step 1: Identify given information - AB = PQ = 5 cm, BC = QR = 7 cm, ∠B = ∠Q = 60°. Step 2: Check which congruence rule applies - Two sides and included angle are equal. Step 3: Apply SAS rule - In △A

Answer

Step 1: Identify triangle type - AB = AC, so triangle ABC is isosceles. Step 2: Apply isosceles triangle property - Angles opposite to equal sides are equal, so ∠B = ∠C. Step 3: Use angle sum property

Answer

Step 1: Find hypotenuses using Pythagoras - AB = √(3² + 4²) = √25 = 5 cm, PQ = √(3² + 4²) = 5 cm. Step 2: Identify given - ∠C = ∠R = 90°, AC = PR = 3 cm, BC = QR = 4 cm, AB = PQ = 5 cm. Step 3: Apply

Answer

Use SSS rule when all three sides of one triangle are equal to corresponding sides of another triangle. Example: Triangle ABC has sides 6 cm, 8 cm, 10 cm. Triangle DEF has sides 6 cm, 8 cm, 10 cm. Sol

Answer

Step 1: Identify the longest side - PR = 9 cm is the longest side. Step 2: Apply theorem - In a triangle, the angle opposite to the longest side is the largest angle. Step 3: Find opposite angle - The

Answer

Step 1: Apply triangle inequality theorem - Sum of any two sides must be greater than the third side. Step 2: Check all combinations - (i) 3 + 7 = 10 < 12 ✗ (ii) 3 + 12 = 15 > 7 ✓ (iii) 7 + 12 = 19 >

Answer

Step 1: Find third angles - In △ABC: ∠C = 180° - 30° - 80° = 70°. In △PQR: ∠R = 180° - 30° - 80° = 70°. Step 2: Identify given information - ∠A = ∠P = 30°, ∠B = ∠Q = 80°, AB = PQ = 6 cm. Step 3: Check

Answer

1. SAS (Side-Angle-Side): Two sides and included angle equal. Example: AB = PQ, ∠B = ∠Q, BC = QR → △ABC ≅ △PQR. 2. ASA (Angle-Side-Angle): Two angles and included side equal. 3. SSS (Side-Side-Side):