Illustrative Mathematics - Geometry - Mathematics - Unit 1 - Lesson 7

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Last updated about 1 year ago

7 Questions

Which of these statements is true?

All squares are regular polygons.

All rhombi are regular polygons.

All rectangles are regular polygons.

All parallelograms are regular polygons.

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This diagram is a straightedge and compass construction of a square BACD (not all markings are shown). The construction followed these steps:
Start with two marked points A and B
Use a straightedge to construct line AB
Use a previous construction to construct a line perpendicular to AB passing through A
Use a previous construction to construct a line perpendicular to AB passing through B
Use a compass to construct a circle centered at A passing through B
Label an intersection point of that circle and the line from step 3 as C
Use a previous construction to construct a line parallel to AB passing through C
Label the intersection of that line and the line from step 4 as D
Use a straightedge to construct the segments AC, CD, and DB

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

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

Construct a segment with the same length as AB with endpoint C.

Construct an equilateral triangle with side CD.

Construct a line through point B perpendicular to AB.

Construct a line through point C perpendicular to CD.

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

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

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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.

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

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This lesson is from Illustrative Mathematics. Geometry, Unit 1, Lesson 7. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/2/1/7/index.html ; accessed 29/July/2021.

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