Lesson 6 Practice Problems

Which of the following constructions would help to construct a line passing through point C that is perpendicular to the line AB?

• Construction of a perpendicular bisector through C

• Construction of a square with one side AB

• Construction of a hexagon with one side BC

• Construction of an equilateral triangle with one side AB

Two distinct lines, l and m, are each perpendicular to the same line n. Select all statements that are true.

• Lines l and m are perpendicular.

• Lines m and n are perpendicular.

• Lines l and n are parallel.

• Lines l and m are parallel.

In a straightedge and compass construction of the bisector of angle BAC, which was the first step necessary?

• Draw a circle centered at B.

• Draw a perpendicular bisector of AB.

• Draw a line parallel to AC.

• Draw a circle centered at A.

Which segment has the same length as segment EA in a perpendicular construction through point C?

• BD

• BE

• ED

• EC

Which triangle is equilateral in the given construction?

• Triangle VWZ is equilateral.

• Triangle STU is equilateral.

In a construction where A is the center of one circle and B is the center of another, which segments have the same length as AB?

• Segment AB

• Segment CD

• Segment BC

• Segment AC

Answer explanation

AC, AD, BC, BD
Both circles are congruent because they share the same radius. Therefore all radii from the circles are congruent.

Name a pair of perpendicular line segments in the construction.

• AM and MB

• AB and CD

• CM and MD

Name a pair of line segments with the same length in the construction.

• AB and CD

• CD and AM

• MD and MB

• AM and BM

A, B, and C are the centers of the 3 circles. Which segment is congruent to AB?

• HA

• CD

• HF

• CE

Which of the following is true if two lines are both perpendicular to a third line?

• They form a triangle.

• They are perpendicular to each other.

• They intersect at a point.

• They are parallel to each other.