Lesson 7 Practice Problems

Which of these statements is true?

• All parallelograms are regular polygons.

• All rectangles are regular polygons.

• All squares are regular polygons.

• All rhombi are regular polygons.

Answer explanation

Regular Polygons

All sides are equal AND all angles are equal.

Why do you need to use a compass to construct a circle centered at 

A passing through B of the square construction?

• To locate point C on the perpendicular line.

• To determine the length of the sides of the square.

• To find the midpoint of AB.

• To ensure the lines are parallel.

To construct a line passing through the point C that is parallel to the line AB, the first step is to create a line through C perpendicular to AB.

What is the next step to construct a line through point C parallel to line AB?

• Construct an equilateral triangle with side CD.

• Construct a line through point B perpendicular to AB.

• Construct a line through point C perpendicular to CD.

• Construct a segment with the same length as AB with endpoint C.

Jada wanted to construct a line perpendicular to line

ℓ through point C. The diagram shows her construction.

What mistake did Jada make in constructing a line perpendicular to line ℓ through point C?

• She did not ensure the lines were perpendicular.

• She used the wrong point as the center.

• She did not construct a perpendicular line through point C.

• She did not use a compass.

Answer explanation

Jada constructed a perpendicular bisector rather than a perpendicular line through point C. The line she drew is perpendicular to ℓ but it does not pass through point C.

What was the first mistake Noah made in his construction to bisect angle BAC?

• He used different radii for the circles.

• He used the wrong points for the centers.

• He didn't notice segments AB and AC have different lengths.

• He did not draw the circles accurately.

Answer explanation

The construction of the bisector of angle BAC starts by drawing a circle with center A and then uses the points where that circle intersects the two rays of angle BAC.

Those two points are equidistant from A. If we use points that are not equidistant from A for the rest of the construction, then it does not bisect the angle as Noah's construction shows.

Here is a straightedge and compass construction.

 If you to draw an equilateral triangle on the figure, how do you know the triangle is equilateral?

• All sides are equal in length.

• It has two equal sides.

• All angles are 90 degrees.

• It has one right angle.

Here are 2 points in the plane.

Explain how to construct a line segment that is half the length of segment AB.

• Use a compass to draw a circle with radius AB.

• Draw a perpendicular bisector of AB.

• Measure AB and draw a new segment with half the length.

• Use a protractor to measure half the angle at A.

Answer explanation

Use a straightedge to draw segment AB.

Draw a circle with center A that passes through B.  Draw a circle with center B that passes through A.

Draw the line through the intersection points of the two circles.

Mark the point where this line intersects segment AB and label it C.  Segment AC is half the length of AB.

Which tool is essential for constructing a perpendicular line?

• Set square

• Ruler

• Protractor

• Compass

What is the first step in constructing an equilateral triangle?

• Draw a circle with a given radius.

• Draw two intersecting lines.

• Draw a perpendicular bisector.

• Draw a line segment of any length.

What is the purpose of using a straightedge in geometric constructions?

• To measure lengths.

• To draw circles.

• To draw straight lines.

• To measure angles accurately.