Construction Techniques 5: Squares

ID: datam-nanod
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Construction Techniques 5: Squares

Classroom:
Due:
Student Name:
Date Submitted:
Problem 1

1) Which of these statements is true?

a) All rectangles are regular polygons. \text{All rectangles are regular polygons. }b) All squares are regular polygons. \text{All squares are regular polygons. }c) All rhombi are regular polygons. \text{All rhombi are regular polygons. }d) All parallelograms are regular polygons.\text{All parallelograms are regular polygons.}
Problem 2

2) This diagram is a straightedge and compass construction of a square BACDBACD (not all markings are shown). The construction followed these steps:

1. Start with two marked points AA and BB

2. Use a straightedge to construct line ABAB

3. Use a previous construction to construct a line perpendicular to ABAB passing through AA

4. Use a previous construction to construct a line perpendicular to ABAB passing through BB

5. Use a compass to construct a circle centered at AA passing through BB

6. Label an intersection point of that circle and the line from step 3 as CC

7. Use a previous construction to construct a line parallel to ABAB passing through CC

8. Label the intersection of that line and the line from step 4 as DD

9. Use a straightedge to construct the segments ACAC, CDCD, and DBDB

Explain why you need to construct a circle in step 5.

A template for answering this question. Ask your instructor for an alternative.
Problem 3

3) To construct a line passing through the point CC that is parallel to the line ABAB, the first step is to create a line through CC perpendicular to ABAB. What is the next step?

A template for answering this question. Ask your instructor for an alternative.
a) Construct an equilateral triangle with side CD\text{Construct an equilateral triangle with side } CD \text{. }b) Construct a line through point B perpendicular to AB\text{Construct a line through point } B \text{ perpendicular to } AB \text{. }c) Construct a segment with the same length as AB with endpoint C\text{Construct a segment with the same length as } AB \text{ with endpoint } C \text{. }d) Construct a line through point C perpendicular to CD.\text{Construct a line through point } C \text{ perpendicular to } CD \text{.}
Problem 4

4) Jada wanted to construct a line perpendicular to line ll through point CC. The diagram shows her construction. What was her mistake?

A template for answering this question. Ask your instructor for an alternative.
Problem 5

5) Noah is trying to bisect angle BACBAC. He draws circles of the same radius with centers BB and CC and then uses one of the points of intersection for his ray. What mistake has Noah made in his construction?

A template for answering this question. Ask your instructor for an alternative.
Problem 6

6) Here is a straightedge and compass construction. Use a straightedge to draw an equilateral triangle on the figure.

A template for answering this question. Ask your instructor for an alternative.

7) Explain how you know the triangle is equilateral.

Problem 7

8) Here are 2 points in the plane. Explain how to construct a line segment that is half the length of segment ABAB.

A template for answering this question. Ask your instructor for an alternative.