## 1. Two triangles are congruent if:

### Answer:

### Explanation:

Two triangles are congruent if both their corresponding sides and angles are equal.

## 2. The criterion that states two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle is:

### Answer:

### Explanation:

SAS stands for Side-Angle-Side.

## 3. In a right-angled triangle, the side opposite to the right angle is called:

### Answer:

### Explanation:

In a right-angled triangle, the side opposite the right angle is the longest side and is called the hypotenuse.

## 4. The angles opposite to equal sides of a triangle are:

### Answer:

### Explanation:

In any triangle, angles opposite to equal sides are equal.

## 5. Which of the following cannot be the sides of a triangle?

### Answer:

### Explanation:

For any triangle, the sum of any two sides must be greater than the third side.

## 6. The sum of all interior angles of a triangle is:

### Answer:

### Explanation:

The sum of all interior angles of any triangle is always 180°.

## 7. If two angles of one triangle are equal to two angles of another triangle, then the triangles are:

### Answer:

### Explanation:

If two angles of one triangle are equal to two angles of another triangle, the third angle will also be equal. Thus, the triangles are similar.

## 8. The ratio of the areas of two similar triangles is equal to the square of the ratio of their:

### Answer:

### Explanation:

If two triangles are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding sides.

## 9. In a ΔABC, if AB = AC, then ∠B is:

### Answer:

### Explanation:

In an isosceles triangle, angles opposite to equal sides are equal.

## 10. If the sides of a triangle are 7 cm, 24 cm, and 25 cm, then the triangle is:

### Answer:

### Explanation:

Using Pythagoras theorem, 7^2 + 24^2 = 25^2. Hence, it's a right-angled triangle.

## 11. If in a ΔABC, AB = AC and BD and CE are bisectors of ∠B and ∠C respectively meeting at O, then:

### Answer:

### Explanation:

In ΔABC, since AB = AC, the angle bisectors will equally divide the angle and meet at the incenter, making OB = OC.

## 12. In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the triangle is:

### Answer:

### Explanation:

This is the Pythagoras theorem, which is valid for right-angled triangles.

## 13. If the medians of a triangle are equal, then the triangle is:

### Answer:

### Explanation:

Only in an equilateral triangle will all three medians be equal.

## 14. The point where the three medians of a triangle meet is called:

### Answer:

### Explanation:

The centroid is the point where the three medians of a triangle intersect.

## 15. If two triangles have the same base and the same area, they must have:

### Answer:

### Explanation:

Area of a triangle is given by (1/2)*base*height. If the base is the same and the area is the same, the height must also be the same.

## 16. If in ΔABC, ∠A = 90° and BD is the altitude, then which of the following is true?

### Answer:

### Explanation:

In a right triangle, the altitude from the right angle bisects the hypotenuse into two unequal parts.

## 17. The triangle with angles 60°, 60°, and 60° is:

### Answer:

### Explanation:

All angles of an equilateral triangle are 60°.

## 18. In a ΔABC, if ∠A = 60°, ∠B = 30°, then ∠C is:

### Answer:

### Explanation:

The sum of all angles in a triangle is 180°. Hence, ∠C = 180° – 60° – 30° = 90°.

## 19. If the sides of a triangle are in the ratio 3:4:5, then the triangle is:

### Answer:

### Explanation:

The sides 3, 4, and 5 form a Pythagorean triplet, indicating a right-angled triangle.

## 20. If the sides of a triangle are in the ratio 1:1:1, then the triangle is:

### Answer:

### Explanation:

All sides being equal indicates an equilateral triangle.