Triangles

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: Let ∠B = ∠C = x. Step …

Answer

Step 1: Identify given information → AB = DE = 4 cm, BC = EF = 3 cm, ∠B = ∠E = 90°. Step 2: Check congruence rule → We have two sides and included angle. Step 3: Apply SAS rule → In △ABC and △DEF: AB …

Answer

Step 1: Identify triangle type → PQ = QR = 7 cm, so triangle PQR is isosceles. Step 2: Property of isosceles triangle → Altitude from vertex angle bisects the base. Step 3: Since QS is altitude to PR,…

Answer

Use ASA when: Two angles and included side of one triangle equal two angles and included side of another triangle. Example: In △ABC and △XYZ, if ∠A = ∠X = 60°, ∠B = ∠Y = 50°, and AB = XY = 5 cm. Step …

Answer

Step 1: Identify triangle type → AB = AC, so isosceles triangle. Step 2: Draw altitude AD to BC → D bisects BC, so BD = DC = 6 cm. Step 3: Use Pythagoras in △ABD → AD² + BD² = AB², so AD² + 6² = 10², …

Answer

Step 1: State the rule → SSS (Side-Side-Side) Congruence Rule. Step 2: Given → In △ABC and △DEF: AB = DE, BC = EF, CA = FD. Step 3: Apply SSS rule → Since all three corresponding sides are equal, △ABC…

Answer

Step 1: Apply Pythagoras theorem → AB² = AC² + BC², so 13² = AC² + 5². Step 2: Calculate AC → 169 = AC² + 25, so AC² = 144, therefore AC = 12 cm. Step 3: Verify dimensions → We have a 5-12-13 right tr…

Answer

Use RHS when: Two right triangles have equal hypotenuse and one equal side. Solution: Step 1: Given → Both triangles have hypotenuse = 10 cm, one side = 6 cm, and one right angle. Step 2: Find third s…