## 1. To divide a line segment in a given ratio, which of the following is essential?

### Answer:

### Explanation:

A compass is essential to mark arcs and create points that help in dividing a line segment in a given ratio.

## 2. How many tangents can be drawn to a circle from an external point?

### Answer:

### Explanation:

Two tangents can be drawn to a circle from an external point, and they are of equal length.

## 3. For constructing an angle of 60°, which instrument is essential?

### Answer:

### Explanation:

Using a compass and straightedge, a 60° angle can be constructed as one of the basic constructible angles.

## 4. If the bisector of an angle divides it into two equal angles, what is the measure of each angle when the original angle is 90°?

### Answer:

### Explanation:

The bisector will divide the 90° angle into two equal parts, each measuring 45°.

## 5. To construct a triangle when its base, a base angle and the difference of the other two sides are given, you would use:

### Answer:

### Explanation:

Using the properties of an angle bisector, one can determine the point where the other two sides meet.

## 6. In the construction of a triangle, if two sides and the included angle are given, it is called:

### Answer:

### Explanation:

This refers to Side-Angle-Side construction of a triangle.

## 7. Which of the following is not a criterion for the construction of a triangle?

### Answer:

### Explanation:

A triangle cannot be constructed uniquely with two sides and a non-included angle.

## 8. To construct the perpendicular bisector of a given line segment, which instrument is necessary?

### Answer:

### Explanation:

A compass is essential to mark arcs from endpoints of the line segment which intersect to give points on the perpendicular bisector.

## 9. If in a circle with center O, a tangent at point A is drawn, which of the following is true?

### Answer:

### Explanation:

The radius at the point of tangency is perpendicular to the tangent, making both statements a) and c) correct.

## 10. To construct an angle of 15°, which other angles are needed?

### Answer:

### Explanation:

By subtracting a 45° angle from a 60° angle, a 15° angle can be constructed.