Lesson 3 Cyclic Polygons Solidify Understanding

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1.

The three angle bisectors of triangle are shown. Use a compass to construct an inscribed circle with center .

Triangle EFG with constructed angle bisectors intersecting at point H.

2.

The three angle bisectors of triangle are shown. Use a compass to construct an inscribed circle with center .

Triangle LMN with constructed angle bisectors intersecting at point O.

3.

The three angle bisectors of triangle are shown. Use a compass to construct an inscribed circle with center .

Triangle TUV with constructed angle bisectors intersecting at point S.

4.

Triangle has an inscribed circle with center . Identify the three segments that are tangent to circle .

Triangle XYZ with inscribed Circle

5.

Triangle has an inscribed circle with center . Identify the three segments that are tangent to circle .

Triangle ABC with inscribed Circle D with angle bisectors constructed.

Set

Find the degree measure of the angle or the intercepted arc indicated in each figure.

6.

with

Circle M with central angle LMN = 110 degrees.

7.

with

Circle B with central angle ABC = 130 degrees and arc DC 130 degrees.

8.

Circle F with arc GH 50 degrees and arc EG 155 degrees.

9.

with diameter

and

Circle M with inscribed angle NLK and NJK.

10.

How can a triangle be used to show the connection between an inscribed angle and the angle measure of the arc it intercepts? What is true about the angle measures in any triangle? What is true about the arc measure for an entire circle?

Go

Write the trigonometric equation needed to find and the trigonometric equation to find in each right triangle.

Then solve for ‌ and .

11.

Right triangle ABC with angle 55 degrees, adjacent leg x, opposite leg 24 in, and hypotenuse y.

12.

Right triangle DEF with angle 28 degrees, adjacent leg 76 cm, opposite leg y, and hypotenuse x.

13.

Right triangle GHK with angle 40 degrees, adjacent leg x, opposite leg y, and hypotenuse 14 m.

14.

Right triangle JLM with angle 37 degrees, adjacent leg x, opposite leg y, and hypotenuse 112 ft.

15.

The Pythagorean theorem could be used to check the side lengths in the previous problems. Examine the Pythagorean theorem for problems 13 and 14 shown.

  • 13:

  • 14:

Explain why the answer in problem 13 doesn’t equal and the answer in problem 14 doesn’t equal .