Unit 7, Lesson 6

A Special Point

Geometry

Practice

Problem 1

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

<p>Quadrilateral A E D F with line A D bisecting angle A into two angles, alpha and beta.</p> — ;

;

Practice

Problem 2

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>

Problem 3

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?

Problem 4

ForLesson 5: Triangles in Circles

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.

Problem 5

ForLesson 5: Triangles in Circles

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

Problem 6

ForLesson 4: Quadrilaterals in Circles

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.

Problem 7

ForLesson 3: Tangent Lines

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>

Problem 8

ForLesson 15: Weighted Averages

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

Problem 9

ForLesson 10: Using Trigonometric Ratios to Find Angles

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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A Special Point

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9