1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson...

26
1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

Transcript of 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson...

Page 1: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

1-5 Segment and Angles Bisectors

Holt Geometry

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Page 2: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

31

4

Warm Up

1. Draw AB and AC, where A, B, and C are noncollinear.

2. Draw opposite rays DE and DF.

Solve each equation.

3. 2x + 3 + x – 4 + 3x – 5 = 180

4. 5x + 2 = 8x – 10

EF D

C

B

APossible answer:

1-5 Segments and Angles Bisectors

Page 3: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Bisect a Segment.

Bisect and Angle

Objectives

1-5 Segments and Angles Bisectors

Page 4: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Midpoint Bisects

Segment Bisector Compass

Straightedge Construct

Construction Midpoint Formula

Angle Bisector

Vocabulary

1-5 Segments and Angles Bisectors

Page 5: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

A segment can be divided into two identical parts using the Midpoint.

In geometry we say that the midpoint bisects a segment if it is equidistant from the endpoints.

An segment bisector is a segment, ray, line or plane that intersects a segment at its midpoint.

1-5 Segments and Angles Bisectors

Page 6: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Activity 1: Construct Segment Bisector

1-5 Segments and Angles Bisectors

Page 7: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

If you know the coordinates of the endpoints of a segment, you can find the coordinates of the midpoint by using the Midpoint Formula:

1-5 Segments and Angles Bisectors

Page 8: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

1-4Angles and Their Measures1-5 Segments and Angles Bisectors

Example 1: Using the Midpoint Formula

Page 9: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

1-4Angles and Their Measures1-5 Segments and Angles Bisectors

Example 1: Using the Midpoint Formula

Page 10: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

An Angle Bisector is a ray that divides and angle into two adjacent angles that are congruent.

1-5 Segments and Angles Bisectors

Page 11: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Activity 1: Construct Angle Bisector

1-5 Segments and Angles Bisectors

Page 12: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

If you know the measure of the bigger angle, we can use the definition of angle bisectors to find the measure of the smaller angles.

1-5 Segments and Angles Bisectors

Example 2: Using Angle Bisectors

Page 13: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

1-5 Segments and Angles Bisectors

Example 2: Using Angle Bisectors

Page 14: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

mDEG = 115°, and EF is the angle bisector. Find mFEG

Example 3: Using the Angle Addition Postulate

mDEG = mDEF + mFEG

115 = 2(mFEG)

57.5 = mFEG

Angle Additions Postulate.

Equality property.

Divide by 2 on both sides.

Simplify.

115 2

1-5 Segments and Angles Bisectors

Page 15: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Check It Out! Example 3

mXWZ = 121° and mXWY = 59°. Find mYWZ.

mYWZ = mXWZ – mXWY

mYWZ = 121 – 59

mYWZ = 62

Add. Post.

Substitute the given values.

Subtract.

1-5 Segments and Angles Bisectors

Page 16: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Example 4: Finding the Measure of an Angle

KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

1-5 Segments and Angles Bisectors

Page 17: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Example 4 Continued

Step 1 Find x.

mJKM = mMKL

(4x + 6)° = (7x – 12)°

+12 +12

4x + 18 = 7x

–4x –4x

18 = 3x

6 = x

Def. of bisector

Substitute the given values.

Add 12 to both sides.

Simplify.

Subtract 4x from both sides.

Divide both sides by 3.

Simplify.

1-5 Segments and Angles Bisectors

Page 18: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Example 4 Continued

Step 2 Find mJKM.

mJKM = 4x + 6

= 4(6) + 6

= 30

Substitute 6 for x.

Simplify.

1-5 Segments and Angles Bisectors

Page 19: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Check It Out! Example 4a Find the measure of each angle.

QS bisects PQR, mPQS = (5y – 1)°, andmPQR = (8y + 12)°. Find mPQS.

5y – 1 = 4y + 6

y – 1 = 6

y = 7

Def. of bisector

Substitute the given values.

Simplify.

Subtract 4y from both sides.

Add 1 to both sides.

Step 1 Find y.

1-5 Segments and Angles Bisectors

Page 20: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Check It Out! Example 4a Continued

Step 2 Find mPQS.

mPQS = 5y – 1

= 5(7) – 1

= 34

Substitute 7 for y.

Simplify.

1-5 Segments and Angles Bisectors

Page 21: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Check It Out! Example 4b

Find the measure of each angle.

JK bisects LJM, mLJK = (-10x + 3)°, andmKJM = (–x + 21)°. Find mLJM.

LJK = KJM

(–10x + 3)° = (–x + 21)°

–9x + 3 = 21

x = –2

Step 1 Find x.

–9x = 18

+x +x

–3 –3

Def. of bisector

Substitute the given values.Add x to both sides.

Simplify.

Subtract 3 from both sides.

Divide both sides by –9.

Simplify.

1-5 Segments and Angles Bisectors

Page 22: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Check It Out! Example 4b Continued

Step 2 Find mLJM.

mLJM = mLJK + mKJM

= (–10x + 3)° + (–x + 21)°

= –10(–2) + 3 – (–2) + 21 Substitute –2 for x.

Simplify.= 20 + 3 + 2 + 21

= 46°

1-5 Segments and Angles Bisectors

Page 23: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Lesson Quiz: Part I

Classify each angle as acute, right, or obtuse.

1. XTS

2. WTU

3. K is in the interior of LMN, mLMK =52°, and mKMN = 12°. Find mLMN.

64°

acute

right

1-5 Segments and Angles Bisectors

Page 24: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Lesson Quiz: Part II

32°

5. Use a protractor to draw an angle with a measure of 165°.

4. BD bisects ABC, mABD = , and

mDBC = (y + 4)°. Find mABC.

1-5 Segments and Angles Bisectors

Page 25: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Lesson Quiz: Part III

6. mWYZ = (2x – 5)° and mXYW = (3x + 10)°. Find the value of x.

35

1-5 Segments and Angles Bisectors

Page 26: 1-5 Segment and Angles Bisectors Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Skills Autonomous

Practice

Pages: 29, 30, 31, 32

1-5 Segments and Angles Bisectors