Construction Techniques 2: Equilateral Triangles

ID: kogam-gugod
Illustrative Mathematics
Subject: Geometry

12 questions

Construction Techniques 2: Equilateral Triangles

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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) ﻿$AC=BC$﻿ b) ﻿$AC=BD$﻿ c) ﻿$CD=AB$﻿ d) ﻿$ABCD$﻿ is a square. 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 ﻿$CD$﻿? Explain your answer.

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 ﻿$B$﻿?

True or false? Write below.

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

True or false? Write below.

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) ﻿$AM=BM$﻿ b) ﻿$CM=DM$﻿ c) ﻿$EA=EM$﻿ d) ﻿$EA﻿ e) ﻿$AM﻿ 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 ﻿$AB$﻿?

a) $CB \text{ }$b) $CD \text{ }$c) $CE \text{ }$d) $CA$