Upload File

inscribed angles section 10-4. an inscribed angle is an angle whose vertex is on a circle and whose...

  • Home
  • Documents
  • Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted
19
Inscribed Angles Section 10-4

Upload: cathleen-bryant

Post on 13-Jan-2016

226 views

Category:

Documents


1 download

Report

TRANSCRIPT

Page 1: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Inscribed Angles

Section 10-4

Page 2: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted arc consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them. A chord or arc subtends an angle if its endpoints lie on the sides of the angle.

Page 3: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted
Page 4: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Find each measure.

Example 1A: Finding Measures of Arcs and Inscribed Angles

mPRU

Inscribed Thm.

Substitute 118 for mPU.

Page 5: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Find each measure.

Example 1B: Finding Measures of Arcs and Inscribed Angles

mSP

Inscribed Thm.

Substitute 27 for m SRP.

Multiply both sides by 2.

Page 6: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Check It Out! Example 1b

Find each measure.

mDAE

Inscribed Thm.

Substitute 76 for mDE.

Page 7: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted
Page 8: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted
Page 9: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Example 3A: Finding Angle Measures in Inscribed Triangles

Find a.

WZY is a right angle WZY is inscribed in a semicircle.

mWZY = 90 Def of rt.

5a + 20 = 90 Substitute 5a + 20 for mWZY.

5a = 70 Subtract 20 from both sides.

a = 14 Divide both sides by 5.

Page 10: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Example 3B: Finding Angle Measures in Inscribed Triangles

Find mLJM.

mLJM = 5(3.5) – 7 = 10.5 Substitute 3.5 for b.

5b – 7 = 3b Substitute the given values.

2b – 7 = 0 Subtract 3b from both sides.

2b = 7 Add 7 to both sides.

b = 3.5 Divide both sides by 2.

mLJM = mLKM mLJM and mLKM

both intercept LM.

Page 11: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Check It Out! Example 3a

Find z.

8z – 6 = 90 Substitute.

8z = 96 Add 6 to both sides.

z = 12 Divide both sides by 8.

ABC is a right angle ABC is inscribed in a semicircle.

mABC = 90 Def of rt.

Page 12: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Check It Out! Example 3b

Find mEDF.

2x + 3 = 75 – 2x Substitute the given values.

4x = 72 Add 2x and subtract 3 from both sides.

x = 18 Divide both sides by 4.

mEDF = 2(18) + 3 = 39°

mEDF = mEGF mEGF and mEDF

both intercept EF.

Page 13: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted
Page 14: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Find the angle measures of GHJK.

Example 4: Finding Angle Measures in Inscribed Quadrilaterals

mG + mJ = 180 GHJK is inscribed in a .3b + 25 + 6b + 20 = 180 Substitute the given values.

9b + 45 = 180 Simplify.

9b = 135 Subtract 45 from both sides.

b = 15 Divide both sides by 9.

Step 1 Find the value of b.

Page 15: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Step 2 Find the measure of each angle.

Example 4 Continued

mG = 3(15) + 25 = 70 Substitute 15 for b

mJ = 6(15) + 20 = 110 in each expression.

mK = 10(15) – 69 = 81mH + mK = 180 H and K are supp.

mH + 81 = 180 Substitute 81 for mK.

mH = 99 Subtract 81 from both sides

Page 16: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Check It Out! Example 4

Find the angle measures of JKLM.

Step 1 Find the value of b.

mM + mK = 180 JKLM is inscribed in a .

Substitute the given values.

10x + 20 = 180

10x = 160

x = 16

4x – 13 + 33 + 6x = 180

Simplify.

Subtract 20 from both sides.

Divide both sides by 10.

Page 17: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Check It Out! Example 4 Continued

mM = 4(16) – 13 = 51

mK = 33 + 6(16) = 129

mJ = 360 – 252 = 108

Step 2 Find the measure of each angle.

Find the angle measures of JKLM.

Page 18: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Lesson Quiz: Part I

Find each measure.

1. RUS

2. a

25°

3

Page 19: Inscribed Angles Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

3. Find the angle measures of ABCD.

Lesson Quiz: Part II

m A = 95°m B = 85°m C = 85° m D = 95°


10 · Web viewInscribed Angle and Intercepted Arc: A C B Theorem 12.11: Inscribed Angle Theorem If an angle is inscribed in a circle, then the measure is half the measure of the intercepted

Miquel Points and Inscribed Triangleseckartschmidt.de/Miqul.pdf · Miquel point, we shall denote the angle ϕ =∠ =∠ =∠ ´ ´ ´ MA B MB C MC A the Miquel angle of the inscribed

Angles Related to a Circle Lesson 10.5. Angles with Vertices on a Circle Inscribed Angle: an angle whose vertex is on a circle and whose sides are determined

Holt McDougal Geometry 11-4 Inscribed Angles Find the measure of an inscribed angle. Use inscribed angles and their properties to solve problems. Objectives

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–3) NGSSS Then/Now New Vocabulary Theorem 10.6: Inscribed Angle Theorem Proof: Inscribed Angle

Inscribed Angles. Inscribed Angles and Central Angles A Central angle has a vertex that lies in the center of a circle. A n inscribed angle has a vertex

6.4Use Inscribed Angles and Polygons Theorem 6.9 Measure of an Inscribed Angle Theorem The measure of an inscribed angle is one half the measure of its

Geometry – Inscribed and Other Angles Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. C B A C A B C

Holt McDougal Geometry 12-4 Inscribed Angles inscribed angle intercepted arc subtend Vocabulary

Chapter 9 Circles - Hanlon Mathhanlonmath.com/pdfFiles/466Chapter9Circles.pdf · 2008-06-23 · An inscribed angle is an angle whose vertex lies on the circle and whose sides contain

Circles Unit Notes 3 Inscribed Angles - celiaroth.weebly.com · Circles Unit Notes 3 Inscribed Angles an angle whose vertex is ON a circle & whose sides are chords the arc that lies

SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than

Inscribed angle and intercepted arc. Find the measure of an inscribed angle. Use inscribed angles and their properties to solve problems. Objectives

Inscribed Angles. An inscribed angle has a vertex on a circle and sides that contain chords of the circle. In, C, QRS is an inscribed angle. An intercepted

Inscribed Angles 10-4. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle

Lesson 6: Unknown Angle Problems with Inscribed Angles … · CORE MATHEMATICS CURRICULUM M5Lesson 6 NYS COMMON GEOMETRY Lesson 6: Unknown Angle Problems with Inscribed Angles in

12.3 Inscribed Angles An angle whose vertex is on the circle and whose sides are chords of the circle is an inscribed angle. An arc with endpoints on the

Lesson 6: Unknown Angle Problems with Inscribed Angles in ... · Lesson 6: Unknown Angle Problems with Inscribed Angles in Circles . Student Outcomes Use the . inscribed angle theorem

Inscribed AnglesInscribed Angles - TypePad · Holt McDougal Geometry Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of

Web viewarc, arc length, central angle, chord, diameter, minor arc, major arc, arc measure, inscribed angle, circumscribed circle, inscribed circle, cyclic quadrilateral, secant, secant

1. 4.2 – Circles & Volume Inscribed Angles Name … · 1. Sec 4.2 – Circles & Volume Inscribed Angles Name: Central Angle: An angle whose vertex is the center of the circle. Inscribed

inscribed angle intercepted arc subtend

Holt Geometry 11-4 Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted

Inscribed Angles - Effingham County Schools / Overvie€¦ · Holt McDougal Geometry Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain

Example - Ms. Virgil's Classroom · 2020. 4. 27. · An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. Un ángulo inscrito es

2019-10-02 12:32 · Inscribed Angle Intercepted Arc Definition An whoso vortex 2 circle and whose contain chords of the circle An arc whoso endpoints lie on the sides of an inscribed

Circles 11 - Ms. Phillips€¦ · 844 Chapter 11 Circles 11 Problem 2 Sitting on the Wheel A central angle is an angle whose vertex is the center of the circle . An inscribed angle

11.4 Inscribed Angles. New Vocab: Inscribed Angle and Intercepted Arc

Today we learned about inscribed angles and …...Today we learned about inscribed angles and inscribed quadrilaterals. Key Concepts: 1. Central Angle = Intercepted Arc 2. Inscribed

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–3) CCSS Then/Now New Vocabulary Theorem 10.6: Inscribed Angle Theorem Proof: Inscribed Angle

my.hrw.com 19.2 Angles in Inscribed Quadrilaterals · 19.2 Angles in Inscribed Quadrilaterals Find each angle measure of the inscribed quadrilateral. Substitute the value of x into

Splash Screen. Vocabulary inscribed angle intercepted arc

Chapter 7: Proportions and Similarity · •Inscribed angle: an angle inside the circle with sides that are chords and a vertex on the edge of the circle •Inscribed angle = ½ intercepted

Geometry Inscribed Angles August 24, 2015 Goals Know what an inscribed angle is. Find the measure of an inscribed angle. Solve problems using inscribed

Central angles, inscribed angles, and intercepted arcs...The Inscribed Angle Theorem states: “The measure of an inscribed angle is half the measure of its intercepted arc.” You