Constructing Angles with a Compass

What is the process of constructing a 90-degree angle using a compass?

• Draw a circle with a radius of 90 units

• Draw two intersecting arcs from the endpoints of a line segment to create a 90-degree angle.

• Use a protractor to measure a 90-degree angle

• Connect three random points to form a 90-degree angle

Explain how to construct a 45-degree angle with a compass.

• Draw a straight line and guess the angle

• Draw a ray, place compass needle on endpoint, draw arc, place needle on intersection, draw another arc, connect endpoint to intersection.

• Draw a circle instead of an angle

• Use a protractor instead of a compass

If you are given a line segment, how can you construct a perpendicular bisector using a compass?

• Create a circle with the segment as the diameter and draw a line tangent to the circle

• Draw a line parallel to the segment passing through one of its endpoints

• Use a protractor to measure the angle and draw a line bisecting it

• Use a compass to draw two intersecting arcs from each end of the line segment, then draw a line connecting the intersection points of the arcs.

Describe the steps to construct a 60-degree angle with a compass.

• Use a compass to draw a straight line and estimate a 60-degree angle visually.

• Construct a 60-degree angle by randomly placing the compass on the paper.

• Use a compass to draw two intersecting arcs from the endpoints of a straight line, creating a 60-degree angle at their intersection.

• Draw a 60-degree angle by connecting three random points with a straight line.

How do you construct a 30-degree angle using a compass?

• Draw a 90-degree angle and bisect it to create a 30-degree angle

• Estimate the angle visually without using any tools

• Use a compass to draw two intersecting arcs from the endpoints of a line segment, creating a 30-degree angle at their intersection.

• Use a protractor to measure a 30-degree angle directly

Explain the method to construct a 120-degree angle with a compass.

• Use a compass to draw two intersecting arcs and connect the intersection points to form a 120-degree angle.

• Create a 120-degree angle by connecting three random points

• Use a protractor to measure the angle directly

• Draw a 90-degree angle and estimate the additional 30 degrees

If you have two intersecting lines, how can you construct an angle bisector using a compass?

• Use arcs and intersecting points to draw the angle bisector.

• Create a perpendicular line to one of the intersecting lines.

• Draw a circle around the intersection point.

• Use only the straightedge of the compass to draw the angle bisector.

Tags

CCSS.HSG.CO.C.9

Describe the steps to construct a 75-degree angle with a compass.

• Construct a ray, draw two intersecting arcs, and the angle between the rays where they intersect is the 75-degree angle.

• Construct a 90-degree angle and then bisect it to get a 75-degree angle

• Draw a straight line and estimate the angle to be 75 degrees

• Use a protractor to measure a 75-degree angle directly

Tags

CCSS.4.MD.C.6

How do you construct a 150-degree angle using a compass?

• Use a protractor to measure and draw a 150-degree angle directly.

• Construct a 150-degree angle by bisecting a 45-degree angle, which is obtained by bisecting a 90-degree angle.

• Construct a 150-degree angle by bisecting a 30-degree angle, which is obtained by bisecting a 60-degree angle.

• Construct a 150-degree angle by bisecting a 75-degree angle, which is obtained by bisecting a 150-degree angle.

Tags

CCSS.4.MD.C.6

Explain the process of constructing a 135-degree angle with a compass.

• Draw a straight line, use a compass to draw two intersecting arcs, and connect the endpoints to form a 135-degree angle.

• Use a protractor to measure a 135-degree angle directly on the paper.

• Construct a 135-degree angle by folding the paper at a specific angle.

• Draw a circle with a compass and randomly connect points to form a 135-degree angle.