# 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