Presentation on theme: "Objectives Students should know 1. How to name and classify angles."— Presentation transcript:
1Objectives Students should know 1. How to name and classify angles. 2. How to use Angle Addition Postulate3, How to use angle bisector..
2Vocabulary Do you know? Angle Vertex Measure Degree Interior of an Angle Exterior of an AngleAcute Angle Obtuse AngleRight Angle Straight AngleCongruent Angle Angle Bisector
3Name the Angles Name each angle in three or more ways. 1. 2. Name three different angles in the figure.
4Classify the AnglesUse the diagram to find the measure of each angle. Then classify each as acute, right, or obtuse.a. BOAb. DOBc. EOCmBOA = 40°BOA is acute.mDOB = 125°DOB is obtuse.mEOC = 105°EOC is obtuse.
5Congruent 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 writeABC DEF.This is read as “angle ABC is congruent to angle DEF.”
6angle bisectorAn angle bisector is a ray that divides an angle into two congruent angles.JK bisects LJM; thus LJK KJM.
8Example 1: Using the Angle Addition Postulate mDEG = 115°, and mDEF = 48°. Find mFEGmDEG = mDEF + mFEG Add. Post.Substitute the given values.Subtract 48 from both sides.Simplify.
9Check it Out: Example 1mXWZ = 121° and mXWY = 59°. Find mYWZ.
10Example 2: Finding the Measure of an Angle KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.
11Example 2 ContinuedStep 1 Find x.mJKM = mMKLDef. of bisectorSubstitute the given values.Add 12 to both sides.Simplify.Subtract 4x from both sides.Divide both sides by 3.Simplify.
12Example 2 ContinuedStep 2 Find mJKM.Substitute 6 for x.Simplify.
13Check It Out! Example 2Find the measure of each angle.JK bisects LJM, mLJK = (-10x + 3)°, andmKJM = (–x + 21)°. Find mLJM.Step 1 Find x.LJK = KJMDef. of bisector(–10x + 3)° = (–x + 21)°Substitute the given values.+x xAdd x to both sides.Simplify.–9x + 3 = 21–3 –3Subtract 3 from both sides.–9x = 18Divide both sides by –9.x = –2Simplify.
14Check It Out! Example 2Step 2 Find mLJM.mLJM = mLJK + mKJM= (–10x + 3)° + (–x + 21)°= –10(–2) + 3 – (–2) + 21Substitute –2 for x.=Simplify.= 46°
15Lesson Quiz: Do you understand the lesson? Independent PracticeTextbook pg 24 #8 and 9Challenge: pg 25 # 30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Homework:1.3 Handout – will be given out once textbook work is checked.