Constructing Patterns

ID: lumun-jagof
Illustrative Math
Subject: Geometry

Constructing Patterns

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Problem 1

1) This diagram was created by starting with points ﻿$A$﻿ and ﻿$B$﻿ and using only straightedge and compass to construct the rest. All steps of the construction are visible. Describe precisely the straightedge and compass moves required to construct the line ﻿$CD$﻿ in this diagram.

Problem 2

2) In the construction, ﻿$A$﻿ is the center of one circle, and ﻿$B$﻿ is the center of the other. Identify all segments that have the same length as segment ﻿$AB$﻿. Write each corresponding letter in the answer box and separate letters with commas.

a) segment ﻿$AC$﻿ ﻿$\quad\quad$﻿ b) segment ﻿$AE$﻿ ﻿$\quad\quad$﻿ c) segment ﻿$BC$﻿ ﻿$\quad\quad$﻿ d) segment ﻿$CD$﻿ ﻿$\quad\quad$﻿ e) segment ﻿$DE$﻿

Problem 3

3) 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 line segments that must have the same length as segment ﻿$AB$﻿. Write each corresponding letter in the answer box and separate letters with commas.

a) ﻿$AB$﻿ ﻿$\quad\quad$﻿ b) ﻿$AC$﻿ ﻿$\quad\quad$﻿ c) ﻿$BC$﻿ ﻿$\quad\quad$﻿ d) ﻿$BD$﻿ ﻿$\quad\quad$﻿ e) ﻿$CD$﻿

Problem 4

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

a) $AB = CD$b) $AB = CE$c) $AB = CF$d) $AB = EF$