## 1. To bisect an angle using a ruler and compass, you should draw:

### Answer:

### Explanation:

By drawing arcs from the sides of the angle which intersect, you find the midpoint which helps in bisecting the angle.

## 2. To construct a perpendicular bisector to a line segment, the arcs in the construction should be drawn with:

### Answer:

### Explanation:

By drawing arcs from both endpoints of the segment that intersect, the perpendicular bisector can be constructed.

## 3. When constructing a triangle given its three sides (SSS), you first:

### Answer:

### Explanation:

You start by drawing one side, then use compass measurements to get the other two sides from the endpoints.

## 4. If you're constructing a triangle given two sides and the included angle (SAS), where do you draw the first arc?

### Answer:

### Explanation:

The arc will determine where the third vertex of the triangle will lie.

## 5. When constructing an angle of 60° using a compass, you essentially construct:

### Answer:

### Explanation:

When you draw an equilateral triangle, all its angles are 60°.

## 6. The construction of a right angle using only a straightedge and compass is equivalent to:

### Answer:

### Explanation:

When you bisect a straight angle (180°), you get a right angle.

## 7. Which of the following cannot be constructed using just a straightedge and compass?

### Answer:

### Explanation:

Some angles, like the 20°, cannot be trisected using only a straightedge and compass.

## 8. In a triangle ABC, if the internal bisector of angle A meets side BC at point D, then the line AD:

### Answer:

### Explanation:

This is a property of the internal angle bisector of a triangle.

## 9. To construct a tangent to a circle from an external point P, you first:

### Answer:

### Explanation:

The tangent at the point where the circle and the line from P to its midpoint intersect is the required tangent.

## 10. To construct an angle of 45°, you first construct:

### Answer:

### Explanation:

Once you've constructed a 90° angle, bisecting it will yield a 45° angle.

## 11. In a triangle ABC, constructing the orthocenter involves finding:

### Answer:

### Explanation:

The orthocenter is the point where all the altitudes of a triangle intersect.

## 12. In a triangle ABC, constructing the circumcenter involves:

### Answer:

### Explanation:

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.

## 13. To construct the bisector of an angle using a compass and straightedge, you should:

### Answer:

### Explanation:

You'll need to use the compass to draw arcs and the straightedge to draw the bisector line.

## 14. To duplicate a given angle, the tool necessary is:

### Answer:

### Explanation:

To duplicate an angle, you'll need to use the compass to transfer lengths and the straightedge to draw lines.

## 15. To trisect a line segment means to:

### Answer:

### Explanation:

Trisecting means dividing something into three equal parts.

## 16. To construct the perpendicular bisector of a given line segment, the necessary tools are:

### Answer:

### Explanation:

The compass is used to mark arcs and the straightedge is used to draw the bisector.

## 17. Which is NOT a basic constructible polygon using only a straightedge and compass?

### Answer:

### Explanation:

While certain heptagons can be constructed, a regular heptagon cannot be constructed using only a straightedge and compass.

## 18. The point where the medians of a triangle intersect is called the:

### Answer:

### Explanation:

The centroid is the point of concurrency of the three medians of a triangle.

## 19. If you need to draw a circle touching all the sides of a triangle, you would be constructing:

### Answer:

### Explanation:

An incircle touches all the sides of a triangle from inside.

## 20. The construction which requires just a straightedge (and not a compass) is:

### Answer:

### Explanation:

Given a point on a line, one can use a straightedge to draw a perpendicular by aligning it appropriately with the given line.