# Lesson Worksheet: Geometric Constructions: Angle Bisectors Mathematics

In this worksheet, we will practice constructing angle bisectors using rulers and compasses without protractors.

**Q1: **

What does the following figure illustrate?

- AAn angle congruent to another angle
- BA bisector of an angle
- CA perpendicular from a point lying outside a straight line
- DA bisector of a line segment
- EA straight line parallel to another line

**Q2: **

True or False: Using only a straight edge, you can construct an angle bisector.

- ATrue
- BFalse

**Q3: **

True or False: By using angle bisectors, we can divide an angle into 2 equal angles.

- AFalse
- BTrue

**Q4: **

Given that is a triangle, use a ruler and the compass to draw the triangle and bisect by the bisector that intersects at . Use the ruler to measure the length of to the nearest decimal.

- A3.7 cm
- B3.2 cm
- C5.2 cm
- D4.2 cm
- E4.7 cm

**Q5: **

Given that is a triangle, use a ruler and a compass to draw the triangle shown and bisect and by the bisectors and that intersect at . Use the ruler to measure the perimeter of the triangle to the nearest decimal.

- A18.4 cm
- B19.1 cm
- C17.9 cm
- D16.9 cm
- E17.6 cm

**Q6: **

Given that is a trapezoid, use a ruler and a compass to draw the trapezoid and bisect by the bisector that intersects at . Use the ruler to measure the length of to the nearest decimal.

- A12.0 cm
- B10.9 cm
- C14.1 cm
- D11.6 cm
- E13.0 cm

**Q7: **

Use a ruler and a compass to draw a triangle , where and , then bisect and by two bisectors that intersect at .

Is equal to ?

- AYes
- BNo

Is equal to ?

- AYes
- BNo

**Q8: **

Given that is an equilateral triangle with side length 4 cm, use a ruler and a compass to draw the triangle and bisect , , and by the bisectors , , and that intersect at point . If intersects at point , use the ruler to measure the length of to the nearest decimal.

- A2.0 cm
- B3.2 cm
- C1.5 cm
- D1.2 cm
- E4.0 cm

**Q9: **

Draw where , , and . Then, draw , , and to bisect , , and , respectively, where cuts at , cuts at , and cuts at . From your observation, which of the following statements is true?

- A is perpendicular to .
- B is perpendicular to .
- C, , and intersect at one point.
- D is perpendicular to .
- EAll of the answers are correct.

**Q10: **

Draw and to create an obtuse angle . Draw to bisect , then draw to bisect and to bisect . From your constructions, which of the following is true?

- A
- B
- C
- D