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9-12 Geometry Unit 1 Lesson 7

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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Modeling Prompts

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 •Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22

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Unit 1, Lesson 7

Construction Techniques 5: Squares

Geometry

Practice

Problem 1

Student Task Statement

Which of these statements is true?

All rectangles are regular polygons.
All squares are regular polygons.
All rhombuses are regular polygons.
All parallelograms are regular polygons.

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Problem 2

Student Task Statement

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

<p>Diagram of construction of square B A C D.</p>

Start with two marked points and .
Use a straightedge to construct line .
Use a previous construction to construct a line perpendicular to passing through .
Use a previous construction to construct a line perpendicular to passing through .
Use a compass to construct a circle centered at passing through .
Label an intersection point of that circle and the line from the third step as .
Use a previous construction to construct a line parallel to passing through .
Label the intersection of that line and the line from the fourth step as .
Use a straightedge to construct the segments , , and .

Explain why you need to construct a circle in the fifth step.

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Problem 3

ForLesson 6: Construction Techniques 4: Parallel and Perpendicular Lines

Student Task Statement

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

<p>Two congruent intersecting circles.</p>

Construct an equilateral triangle with side .

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Problem 4

ForLesson 6: Construction Techniques 4: Parallel and Perpendicular Lines

Student Task Statement

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

<p>Two circles that pass through each others centers.</p>

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Problem 5

ForLesson 5: Construction Techniques 3: Perpendicular Lines and Angle Bisectors

Student Task Statement

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

<p>Angle B A C. B and C are centers of two congruent and overlapping circles. A ray is drawn from point A through one of the points of intersection of the circles.</p>

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Problem 6

ForLesson 4: Construction Techniques 2: Equilateral Triangles

Student Task Statement

Here is a straightedge and compass construction. Use a straightedge to draw an equilateral triangle on the figure. Explain how you know the triangle is equilateral.

<p>Seven equal radius circles with one in the center and six centered evenly around the center circle.</p>

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Problem 7

ForLesson 3: Construction Techniques 1: Perpendicular Bisectors

Student Task Statement

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

<p>Two points, A and B.</p>

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Lesson 7 Resources

Student Materials

Construct a line through point perpendicular to .

Construct a segment with the same length as with endpoint .

Construct a line through point perpendicular to .