# Construction Techniques 2: Equilateral Triangles

# Construction Techniques 2: Equilateral Triangles

##### Problem 1

1) 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.

##### Problem 2

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

##### Problem 3

3) 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. Write each corresponding letter in the answer box and separate letters with commas.

a) $AC=BC$ $\quad\quad$ b) $AC=BD$ $\quad\quad$ c) $CD=AB$ $\quad\quad$ d) $ABCD$ is a square. $\quad\quad$ e) $ABD$ is an equilateral triangle.

f) $CD=AB+AB$

##### Problem 4

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

##### Problem 5

Here are 2 points in the plane.

5) Using only a straightedge, can you find points in the plane that are the same distance from points $A$ and $B$?

6) Explain your reasoning.

7) Using only a compass, can you find points in the plane that are the same distance from points $A$ and $B$?

8) Explain your reasoning.

##### Problem 6

9) 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. Write each corresponding letter in the answer box and separate letters with commas.

a) $AM=BM$ $\quad\quad$ b) $CM=DM$ $\quad\quad$ c) $EA=EM$ $\quad\quad$ d) $EA<EB$ $\quad\quad$ e) $AM<AB$ $\quad\quad$ f) $AM>BM$

##### Problem 7

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

##### Problem 8

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

##### Problem 9

12) 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 $AB$?