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**Objectives Students should know 1. How to name and classify angles.**

2. How to use Angle Addition Postulate 3, How to use angle bisector..

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**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

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**Name the Angles Name each angle in three or more ways. 1. 2. **

Name three different angles in the figure.

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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 mBOA = 40° BOA is acute. mDOB = 125° DOB is obtuse. mEOC = 105° EOC is obtuse.

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**Congruent angles are angles that have the same measure.**

Arc marks are used to show that the two angles are congruent. mABC = mDEF, so you can write ABC DEF. This is read as “angle ABC is congruent to angle DEF.”

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angle bisector An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK KJM.

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**Example 1: Using the Angle Addition Postulate**

mDEG = 115°, and mDEF = 48°. Find mFEG mDEG = mDEF + mFEG Add. Post. Substitute the given values. Subtract 48 from both sides. Simplify.

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Check it Out: Example 1 mXWZ = 121° and mXWY = 59°. Find mYWZ.

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**Example 2: Finding the Measure of an Angle**

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

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Example 2 Continued Step 1 Find x. mJKM = mMKL Def. of bisector Substitute the given values. Add 12 to both sides. Simplify. Subtract 4x from both sides. Divide both sides by 3. Simplify.

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Example 2 Continued Step 2 Find mJKM. Substitute 6 for x. Simplify.

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Check It Out! Example 2 Find the measure of each angle. JK bisects LJM, mLJK = (-10x + 3)°, and mKJM = (–x + 21)°. Find mLJM. Step 1 Find x. LJK = KJM Def. of bisector (–10x + 3)° = (–x + 21)° Substitute the given values. +x x Add x to both sides. Simplify. –9x + 3 = 21 –3 –3 Subtract 3 from both sides. –9x = 18 Divide both sides by –9. x = –2 Simplify.

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Check It Out! Example 2 Step 2 Find mLJM. mLJM = mLJK + mKJM = (–10x + 3)° + (–x + 21)° = –10(–2) + 3 – (–2) + 21 Substitute –2 for x. = Simplify. = 46°

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**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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