Illustrative Mathematics - Geometry - Mathematics - Unit 1 - Lesson 4

This diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other. Explain how we know triangle ABC is equilateral.

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A, B, and C are the centers of the 3 circles. How many equilateral triangles are there in this diagram?

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This diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other. Select all the true statements.

• {"blocks":[{"key":"3oquj","text":"AC = BC","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":0,"length":2,"style":"BOLD"},{"offset":5,"length":2,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"89mbc","text":"AC = BD","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":0,"length":2,"style":"BOLD"},{"offset":5,"length":2,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"bn0ag","text":"CD = AB","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":0,"length":3,"style":"BOLD"},{"offset":4,"length":3,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"2bc72","text":"ABCD is a square","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":0,"length":5,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"du8ol","text":"ABD is an equilateral triangle","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":0,"length":3,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}

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Line segment CD is the perpendicular bisector of line segment AB. Is line segment AB the perpendicular bisector of line segment CD?

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In this diagram, line segment CD is the perpendicular bisector of line segment AB. Assume the conjecture that the set of points equidistant from A and B is the perpendicular bisector of AB is true. Select all statements that must be true. AB \perp CD

• AM = BM
• CM - DM
• EA = EM
• EA < EB
• AM < AB

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he diagram was constructed with straightedge and compass tools. Name all segments that have the same length as segment AC.

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Starting with 2 marked points, A and B, precisely describe the straightedge and compass moves required to construct the quadrilateral ACBD in this diagram.

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In the construction, A is the center of one circle and B is the center of the other. Which segment has the same length as AB?

• CB
• CD
• CE
• CA

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