# Construction Techniques 1: Perpendicular Bisectors

ID: sohoh-hiris
Illustrative Mathematics
Subject: Geometry

6 questions

# Construction Techniques 1: Perpendicular Bisectors

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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. Select all the true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) Line ﻿$CD$﻿ is perpendicular to segment ﻿$AB$﻿ b) Point ﻿$M$﻿ is the midpoint of segment ﻿$AB$﻿

c) The length ﻿$AB$﻿ is equal to the length ﻿$CD$﻿ d) Segment ﻿$AM$﻿ is perpendicular to segment e) ﻿$CB + BD > CD$﻿

##### Problem 2

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.

2) Is point ﻿$E$﻿ closer to point ﻿$A$﻿, closer to point ﻿$B$﻿, or the same distance between the points?

3) Explain how you know.

##### Problem 3

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

##### Problem 4

5) This diagram was created by starting with points ﻿$C$﻿ and ﻿$D$﻿ and using only straightedge and compass to construct the rest. All steps of the construction are visible. Select all the steps needed to produce this diagram. Write each corresponding letter in the answer box and separate letters with commas.

a) Construct a circle centered at ﻿$A$﻿. b) Construct a circle centered at ﻿$C$﻿. c) Construct a circle centered at ﻿$D$﻿.

d) Label the intersection points of the circles ﻿$A$﻿ and ﻿$B$﻿. e) Draw the line through points ﻿$C$﻿ and ﻿$D$﻿.

f) Draw the line through points ﻿$A$﻿ and ﻿$B$﻿.

##### Problem 5

6) This diagram was constructed with straightedge and compass tools. ﻿$A$﻿ is the center of one circle, and ﻿$C$﻿ is the center of the other. Select all true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) ﻿$AB = BC$﻿ b) ﻿$AB = BD$﻿ c) ﻿﻿ ﻿$AD = 2AC$﻿ d) ﻿$BC = CD$﻿ e) ﻿$BD = CD$﻿