# Build It

ID: juzag-sojon
Illustrative Mathematics, CC BY 4.0
Subject: Geometry

6 questions

# Build It

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##### Problem 1

1) Here is a diagram of a straightedge and compass construction. ﻿$C$﻿ is the center of one circle, and ﻿$B$﻿ is the center of the other. Explain why the length of segment ﻿$BD$﻿ is the same as the length of segment ﻿$AB$﻿.

##### Problem 2

2) Clare used a compass to make a circle with a radius the same length as segment ﻿$AB$﻿. She labeled the center ﻿$C$﻿. Which statement is true?

a)

﻿$AB>CD$﻿

b)

﻿$AB$﻿=﻿$CD$﻿

c)

﻿$AB>CE$﻿

d)

﻿$AB$﻿=﻿$CE$﻿

##### Problem 3

3) The diagram was constructed with straightedge and compass tools. Points ﻿$A$﻿, ﻿$B$﻿, ﻿$C$﻿, ﻿$D$﻿, and ﻿$E$﻿ are all on line segment ﻿$CD$﻿. Name a line segment that is half the length of ﻿$CD$﻿.

4) Explain how you know.

##### Problem 4

This diagram was constructed with straightedge and compass tools. ﻿$A$﻿ is the center of one circle, and ﻿$C$﻿ is the center of the other.

5) The 2 circles intersect at point ﻿$B$﻿. Label the other intersection point ﻿$E$﻿.

6) How does the length of segment ﻿$CE$﻿ compare to the length of segment ﻿$AD$﻿?