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

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Presentation transcript:

Objectives Students should know 1. How to name and classify angles. 2. How to use Angle Addition Postulate 3, How to use angle bisector..

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

Name the Angles Name each angle in three or more ways. 1. 2. 1. 2. Name three different angles in the figure.

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° BOA is acute. mDOB = 125° DOB is obtuse. mEOC = 105° EOC is obtuse.

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.”

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

Example 1: Using the Angle Addition Postulate mDEG = 115°, and mDEF = 48°. Find mFEG mDEG = mDEF + mFEG  Add. Post. Substitute the given values. Subtract 48 from both sides. Simplify.

Check it Out: Example 1 mXWZ = 121° and mXWY = 59°. Find mYWZ.

Example 2: Finding the Measure of an Angle KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

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.

Example 2 Continued Step 2 Find mJKM. Substitute 6 for x. Simplify.

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. 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.

Check It Out! Example 2 Step 2 Find mLJM. mLJM = mLJK + mKJM = (–10x + 3)° + (–x + 21)° = –10(–2) + 3 – (–2) + 21 Substitute –2 for x. = 20 + 3 + 2 + 21 Simplify. = 46°

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.