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9-12 Geometry Unit 7 Lesson 6

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

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

Unit

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 •Unit 7 Unit 8

Modeling Prompts

Lesson

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

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

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

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Unit 7, Lesson 6

A Special Point

Geometry

Practice

Problem 1
Student Task Statement

How do the values of and compare? Explain your reasoning.

;

;

Quadrilateral A E D F with line A D bisecting angle A into two angles, alpha and beta. Line A D creates 2 triangles, A D E and A D F. Angle E and F are right angles. D F is 3 units, D E is 3 units.

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Problem 2

Student Task Statement

Triangle is shown together with its angle bisectors. Draw a point that is equidistant from sides and , but that is closest to side .

<p>Triangle A B C with angle bisectors that intersect in the center of the triangle.</p>

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Problem 3

Student Task Statement

In triangle , point is the incenter. Sketch segments to represent the distance from point to the sides of the triangle. How must these distances compare?

<p>Triangle ABC with incenter D</p>

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Problem 4

ForLesson 5: Triangles in Circles

Student Task Statement

Triangle has circumcenter .

Sketch the 3 lines that intersect at the circumcenter.
If the distance from point to point is 5 units, what is the distance from point to point ? Explain or show your reasoning.

<p>Triangle ABC with circumcenter D</p>

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Problem 5

ForLesson 5: Triangles in Circles

Student Task Statement

The angles of triangle measure 50 degrees, 40 degrees, and 90 degrees. Will its circumcenter fall inside the triangle, on the triangle, or outside the triangle?

inside the triangle
on the triangle
outside the triangle

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Problem 6

ForLesson 4: Quadrilaterals in Circles

Student Task Statement

Tyler and Kiran are discussing the parallelogram in the image. Tyler says the parallelogram cannot be cyclic. Kiran says the parallelogram can be cyclic if a circle is drawn carefully through the vertices.

<p>Parallelogram with one angle measuring 20 degrees.</p>

Do you agree with either of them? Explain or show your reasoning.

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Problem 7

ForLesson 3: Tangent Lines

Student Task Statement

Find the measures of the remaining angles of quadrilateral .

<p>Circle with center W. Radii W X and W Z shown. Segments X Y and Y Z are tangent to the circle. Angle X Y Z is 70 degrees.</p>

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Problem 8

ForLesson 15: Weighted Averages

Student Task Statement

Which expression describes a point that partitions a segment in a ratio?

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Problem 9

ForLesson 10: Using Trigonometric Ratios to Find Angles

Student Task Statement

Write three expressions that can be used to find angle .

<p>Right triangle abc. Side AB =48 units, side BC=55 units, side CA = 73 units </p>

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Lesson 6 Resources

Student Materials