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Holt McDougal Geometry 1-3 Measuring and Constructing Angles Objectives Students should know 1. How to name and classify angles. 2. How to use Angle Addition.

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Presentation on theme: "Holt McDougal Geometry 1-3 Measuring and Constructing Angles Objectives Students should know 1. How to name and classify angles. 2. How to use Angle Addition."— Presentation transcript:

1 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Objectives Students should know 1. How to name and classify angles. 2. How to use Angle Addition Postulate 3, How to use angle bisector..

2 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Vocabulary Do you know? Angle Vertex Measure Degree Interior of an Angle Exterior of an Angle Acute Angle Obtuse Angle Right Angle Straight Angle Congruent Angle Angle Bisector

3 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Name the Angles Name each angle in three or more ways Name three different angles in the figure.

4 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Classify the Angles Use the diagram to find the measure of each angle. Then classify each as acute, right, or obtuse. a. BOA b. DOB c. EOC mBOA = 40° mDOB = 125° mEOC = 105° BOA is acute. DOB is obtuse. EOC is obtuse.

5 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Congruent angles are angles that have the same measure. Arc marks are used to show that the two angles are congruent. mABC = mDEF, so you can write ABC  DEF. This is read as “angle ABC is congruent to angle DEF.”

6 Holt McDougal Geometry 1-3 Measuring and Constructing Angles An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK  KJM. angle bisector

7 Holt McDougal Geometry 1-3 Measuring and Constructing Angles

8 Holt McDougal Geometry 1-3 Measuring and Constructing Angles mDEG = 115°, and mDEF = 48°. Find mFEG Example 1: Using the Angle Addition Postulate mDEG = mDEF + mFEG Add. Post. Substitute the given values. Subtract 48 from both sides. Simplify.

9 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Check it Out: Example 1 mXWZ = 121° and mXWY = 59°. Find mYWZ.

10 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 2: Finding the Measure of an Angle KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

11 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 2 Continued Step 1 Find x. mJKM = mMKL Def. of  bisector Substitute the given values. Add 12 to both sides. Simplify. Subtract 4x from both sides. Divide both sides by 3. Simplify.

12 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Example 2 Continued Step 2 Find mJKM. Substitute 6 for x. Simplify.

13 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Check It Out! Example 2 Find the measure of each angle. JK bisects LJM, mLJK = (-10x + 3)°, and mKJM = (–x + 21)°. Find mLJM. LJK = KJM (–10x + 3)° = (–x + 21)° –9x + 3 = 21 x = –2 Step 1 Find x. –9x = 18 +x +x –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.

14 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Check It Out! Example 2 Step 2 Find mLJM. mLJM = mLJK + mKJM = (–10x + 3)° + (–x + 21)° = –10(–2) + 3 – (–2) + 21Substitute –2 for x. Simplify.= = 46°

15 Holt McDougal Geometry 1-3 Measuring and Constructing Angles Lesson Quiz: Do you understand the lesson? Independent Practice Textbook pg 24 #8 and 9 Challenge: pg 25 # 30 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Homework: 1.3 Handout – will be given out once textbook work is checked.


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