Triangles

8 cm

Step 1: Given right triangle ABC with right angle at C, AB = 10 cm (hypotenuse), BC = 6 cm. Step 2: Apply Pythagoras theorem: AB² = AC² + BC². Step 3: Substitute values: 10² = AC² + 6², which gives 100 = AC² + 36. Step 4: Solve for AC: AC² = 100 - 36 = 64, so AC = √64 = 8 cm.

RHS rule

Step 1: Given two right triangles with equal hypotenuse (13 cm each) and one equal side (5 cm each). Step 2: Both triangles have a right angle (90°). Step 3: RHS (Right angle-Hypotenuse-Side) congruence rule states that if hypotenuse and one side of one right triangle equal hypotenuse and one side of another right triangle, they are congruent. Step 4: Since we have equal hypotenuses and one equal side in both right triangles, they are congruent by RHS rule.

35°

Step 1: Given triangle PQR with PQ = PR (isosceles triangle) and angle Q = 35°. Step 2: In an isosceles triangle, angles opposite to equal sides are equal. Step 3: Since PQ = PR, the angles opposite to these sides are angle R and angle Q respectively. Step 4: Therefore, angle R = angle Q = 35°.

70°

Step 1: Given triangles ABC and DEF are congruent by ASA rule with angle A = 60°, AB = 8 cm, angle B = 70°. Step 2: For ASA congruence, the correspondence is typically A ↔ D, B ↔ E, C ↔ F when sides AB and DE are equal. Step 3: In congruent triangles, corresponding angles are equal. Step 4: Since angle B corresponds to angle E, angle E = angle B = 70°.