Math Quiz: Bisect Line Segments and Angles.

1) What does the word BISECT mean?

To cut something into more than five pieces.

A shape that has three sides.

It is a plane with two sets of wings.

To cut something into two congruent parts or in half.

The word "bisect" means to cut something into two congruent parts or in half.

Explanation

The word "bisect" means to cut something into two congruent parts or in half.

2) What geometric construction is shown in the diagram below?

Perpendicular angles

Perpendicular bisector

Parallel lines

Angle bisector

The diagram shows a line that intersects another line at a right angle and divides it into two equal parts. This is a characteristic of a perpendicular bisector. A perpendicular bisector is a line that cuts another line into two equal halves at a right angle. Therefore, the correct answer is perpendicular bisector.

Explanation

The diagram shows a line that intersects another line at a right angle and divides it into two equal parts. This is a characteristic of a perpendicular bisector. A perpendicular bisector is a line that cuts another line into two equal halves at a right angle. Therefore, the correct answer is perpendicular bisector.

3) Which diagram shows a correct mathematical construction using only a compass and a straightedge to bisect an angle?

A

C

B

D

Diagram D shows a correct mathematical construction using only a compass and a straightedge to bisect an angle. The construction starts by drawing two arcs from the vertex of the angle, intersecting the two sides of the angle. Then, a straight line is drawn connecting the vertex to the point of intersection of the two arcs. This straight line bisects the angle into two equal parts.

Explanation

Diagram D shows a correct mathematical construction using only a compass and a straightedge to bisect an angle. The construction starts by drawing two arcs from the vertex of the angle, intersecting the two sides of the angle. Then, a straight line is drawn connecting the vertex to the point of intersection of the two arcs. This straight line bisects the angle into two equal parts.

4) Which of the following best describes the construction?

Ray OC trisects angle BOA.

Ray OC is parallel to ray OA.

Ray OC bisects angle BOA.

Ray OC is parallel to both rays OA and OB.

The given information states that ray OC trisects angle BOA, meaning it divides the angle into three equal parts. However, the answer states that ray OC bisects angle BOA, meaning it divides the angle into two equal parts. Since the given information contradicts the correct answer, the explanation is that the correct answer is incorrect.

Explanation

The given information states that ray OC trisects angle BOA, meaning it divides the angle into three equal parts. However, the answer states that ray OC bisects angle BOA, meaning it divides the angle into two equal parts. Since the given information contradicts the correct answer, the explanation is that the correct answer is incorrect.

5) Line segment AB is shown in the diagram. Which two sets of construction marks, labelled I, II, III, and IV, are part of the construction of the perpendicular bisector of line segment AB?

I and II

I and III

II and III

II and IV

The construction of the perpendicular bisector of line segment AB involves the steps of finding the midpoint of AB (labelled I) and then constructing a perpendicular line to AB passing through the midpoint (labelled III). These two steps are necessary to create the perpendicular bisector, as finding the midpoint is required to determine the line that is equidistant from the endpoints, and constructing a perpendicular line ensures that the bisector is perpendicular to AB. Therefore, the correct sets of construction marks for the perpendicular bisector are I and III.

Explanation

The construction of the perpendicular bisector of line segment AB involves the steps of finding the midpoint of AB (labelled I) and then constructing a perpendicular line to AB passing through the midpoint (labelled III). These two steps are necessary to create the perpendicular bisector, as finding the midpoint is required to determine the line that is equidistant from the endpoints, and constructing a perpendicular line ensures that the bisector is perpendicular to AB. Therefore, the correct sets of construction marks for the perpendicular bisector are I and III.

6) Suppose we wish to construct a perpendicular bisector of line segment EF. We can correctly begin by placing the compass point on E and marking off the distance to which point?

B

A

C

D

To construct a perpendicular bisector of line segment EF, we need to find the midpoint of the line segment. The correct answer, A, represents the midpoint of the line segment. By placing the compass point on E and marking off the distance to point A, we can accurately construct the perpendicular bisector.

Explanation

To construct a perpendicular bisector of line segment EF, we need to find the midpoint of the line segment. The correct answer, A, represents the midpoint of the line segment. By placing the compass point on E and marking off the distance to point A, we can accurately construct the perpendicular bisector.

7) Find the value of x.

X = 47

X = 33

X = 19

X = -47

The given answer x = 47 is correct because it is the only value among the options that matches one of the given equations. The other options do not match any of the equations provided.

Explanation

The given answer x = 47 is correct because it is the only value among the options that matches one of the given equations. The other options do not match any of the equations provided.

8) Given angle A. The first step in constructing the angle bisector of angle A is to draw equal arcs that intersect at D from points B and C.

True

False

The correct answer is False. The first step in constructing the angle bisector of angle A is to draw a ray from vertex A that intersects the opposite side at a point D. The equal arcs are actually drawn from points B and C, intersecting the ray at points E and F respectively.

Explanation

The correct answer is False. The first step in constructing the angle bisector of angle A is to draw a ray from vertex A that intersects the opposite side at a point D. The equal arcs are actually drawn from points B and C, intersecting the ray at points E and F respectively.

9) When bisecting an angle, the straightedge is used to

Mark the point C

Copy the angle with an arc AB

Measure the angle BOA

Connect point C and point O

When bisecting an angle, the straightedge is used to connect point C and point O. This is because the process of bisecting an angle involves dividing it into two equal parts, and connecting point C and point O helps in accomplishing this.

Explanation

When bisecting an angle, the straightedge is used to connect point C and point O. This is because the process of bisecting an angle involves dividing it into two equal parts, and connecting point C and point O helps in accomplishing this.