Altitudes and Medians of a Triangle (त्रिकोणाची उंची आणि मध्यगा) MCQ Test — Class 8 Maharashtra SSC

Solution:

The angle sum property states that the sum of all interior angles of any triangle is always 180°.

This can be proven by drawing a line parallel to the base through the opposite vertex. — ∠A + ∠B + ∠C = 180°

Solution:

We know the angle sum property: — ∠A + ∠B + ∠C = 180°

Substitute the known angles: — 65° + 45° + ∠C = 180°

Simplify: — 110° + ∠C = 180°

Solve for the third angle: — ∠C = 180° - 110° = 70°

Solution:

A triangle classified by its sides:

Equilateral: All 3 sides are equal (and all angles are 60°)

Isosceles: Exactly 2 sides are equal

Scalene: No sides are equal

Solution:

In an equilateral triangle, all angles are equal. Let each angle be x.

Using the angle sum property: — x + x + x = 180°

Solving: — 3x = 180° → x = 60°

Solution:

Classification by angles:

Right triangle: One angle is exactly 90°

Acute triangle: All angles are less than 90°

Obtuse triangle: One angle is greater than 90°

Solution:

In a right triangle, one angle is 90°.

The sum of all angles: — 90° + 35° + x = 180°

So the other acute angle: — x = 180° - 90° - 35° = 55°

Solution:

An isosceles triangle has exactly 2 equal sides.

The angles opposite to the equal sides are also equal (base angles).

Solution:

The Exterior Angle Theorem states:

An exterior angle of a triangle equals the sum of the two non-adjacent (remote) interior angles. — Exterior angle = ∠A + ∠B (where ∠C is adjacent)

Solution:

If two angles are 90° each, their sum alone would be: — 90° + 90° = 180°

This leaves 0° for the third angle, which is impossible.

Therefore, a triangle cannot have two right angles.

Solution:

Triangle Inequality: Sum of any two sides must be greater than the third side.

Check 4, 5, 7: — 4 + 5 = 9 > 7 ✓, 4 + 7 = 11 > 5 ✓, 5 + 7 = 12 > 4 ✓

Check 3, 4, 8: — 3 + 4 = 7 < 8 ✗ (fails!)