Geometry | Unit 1 | Lesson 4: Construction Techniques 2: Equilateral Triangles | Practice Problems

This diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other. Explain how we know triangle ABC is equilateral.

A, B, and C are the centers of the 3 circles. How many equilateral triangles are there in this diagram?

This diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other. Select all the true statements.

• ABCD is a square.

• CD=AB

• ABD is an equilateral triangle.

• AC=BD

• AC=BC

Line segment CD is the perpendicular bisector of line segment AB. Is line segment AB the perpendicular bisector of line segment CD?

Here are 2 points in the plane. Using only a straightedge, can you find points in the plane that are the same distance from points A and B? Explain your reasoning.

Using only a compass, can you find points in the plane that are the same distance from points A and B? Explain your reasoning.

In this diagram, line segment CD is the perpendicular bisector of line segment AB. Assume the conjecture that the set of points equidistant from A and B is the perpendicular bisector of AB is true. Select all statements that must be true.

• A M = B M

• A M < A B

• C M = D M

• E A < E B

• E A = E M

The diagram was constructed with straightedge and compass tools. Name all segments that have the same length as segment AC.

Starting with 2 marked points, A and B, precisely describe the straightedge and compass moves required to construct the quadrilateral ACBD in this diagram.

In the construction, A is the center of one circle and B is the center of the other. Which segment has the same length as AB?

• CB

• CD

• CE

• CA