1. Problem: Given three sides of a triangle: 5 m, 5 m, and 8 m. Step 1: Identify the type of triangle by comparing side lengths. Step 2: Recall definitions: - Equilateral: all sides equal. - Isosceles: two sides equal. - Scalene: all sides different. Step 3: Compare sides: 5 m = 5 m, 8 m different. Step 4: Since two sides are equal, the triangle is isosceles. 2. Problem: Triangle with angles 40°, 70°, and 70°. Step 1: Classify by angles: - Acute: all angles < 90° - Right: one angle = 90° - Obtuse: one angle > 90° Step 2: All angles are less than 90°, so the triangle is acute. 3. Problem: Triangle with two angles 65° and 55°. Step 1: Find third angle using sum of angles in triangle = 180°. Step 2: Calculate third angle: $$180 - (65 + 55) = 180 - 120 = 60$$ degrees. Step 3: Classify by angles: all angles (65°, 55°, 60°) are less than 90°, so acute triangle. 4. Problem: Triangle with exterior angle 120° and one opposite interior angle 50°. Step 1: Exterior angle equals sum of two opposite interior angles. Step 2: Let other opposite interior angle be $x$. Step 3: Write equation: $$120 = 50 + x$$ Step 4: Solve for $x$: $$x = 120 - 50 = 70$$ degrees. Step 5: Verify sum of interior angles: $$50 + 70 + (180 - 120) = 50 + 70 + 60 = 180$$ degrees, which is correct. 5. Problem: Two sides 7 m and 10 m, test third sides 5 m, 9 m, 17 m for triangle formation. Step 1: Triangle inequality rule: sum of any two sides > third side. Step 2: Test 5 m: - 7 + 5 = 12 > 10 (ok) - 7 + 10 = 17 > 5 (ok) - 5 + 10 = 15 > 7 (ok) Step 3: Test 9 m: - 7 + 9 = 16 > 10 (ok) - 7 + 10 = 17 > 9 (ok) - 9 + 10 = 19 > 7 (ok) Step 4: Test 17 m: - 7 + 17 = 24 > 10 (ok) - 7 + 10 = 17 = 17 (not greater, fails) - 10 + 17 = 27 > 7 (ok) Step 5: Since 7 + 10 is not greater than 17, 17 m cannot form a triangle. Final answers: 1a. Isosceles 1b. Two sides equal (5 m, 5 m), one different (8 m). 2a. Acute triangle 2b. All angles less than 90° 3a. Third angle is 60° 3b. Acute triangle 4a. Other opposite interior angle is 70° 4b. Sum of interior angles is 180° 5a. 17 m cannot form a triangle 5b. Violates triangle inequality rule