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One Perpendicular Bisector

Unit 7 ● Lesson 5 ● Activity 1

Use a straightedge to make a triangle like the one shown.

Construct the perpendicular bisector of segment AB.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Warm-up

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Triangles in Circles

Unit 7

Lesson 5

Circles

GEOMETRY

3 of 8

Unit 7 ● Lesson 5

I can construct the circumscribed circle of a triangle.
I can explain why the perpendicular bisectors of a triangle’s sides meet at a single point.

Learning

Targets

Geometry

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Three Perpendicular Bisectors

Unit 7 ● Lesson 5 ● Activity 2

Construct the perpendicular bisector of segment BC from the earlier activity. Label the point where the 2 perpendicular bisectors intersect as P.

Construct a circle centered at P with radius PA.

Why does the circle also pass through points B and C?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

5 of 8

circumcenter

Unit 7 ● Lesson 5

The circumcenter of a triangle is the intersection of all three perpendicular bisectors of the triangle’s sides. It is the center of the triangle’s circumscribed circle.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Glossary

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Wandering Centers

Unit 7 ● Lesson 5 ● Activity 3

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

7 of 8

Wandering Centers

Unit 7 ● Lesson 5 ● Activity 3

Move the vertices of triangle ABC and observe the resulting location of the triangle’s circumcenter, point D. Determine what seems to be true when the circumcenter is in each of these locations:

outside the triangle
on one of the triangle’s sides
inside the triangle

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

8 of 8

Triangles in Circles

Unit 7 ● Lesson 5

The points represent locations of 3 research stations in a desert, and that scientists want to build a supply hut that is the same distance from all 3 stations. What should they do?

The scientists want to build another research station the same distance from the supply hut as the other stations. What should they do?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Lesson Synthesis