Presentation on theme: "Objectives Students should know 1. How to name and classify angles."— Presentation transcript:
1 Objectives Students should know 1. How to name and classify angles. 2. How to use Angle Addition Postulate3, How to use angle bisector..
2 Vocabulary Do you know? Angle Vertex Measure Degree Interior of an Angle Exterior of an AngleAcute Angle Obtuse AngleRight Angle Straight AngleCongruent Angle Angle Bisector
3 Name the Angles Name each angle in three or more ways. 1. 2. Name three different angles in the figure.
4 Classify 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.
5 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 writeABC DEF.This is read as “angle ABC is congruent to angle DEF.”
6 angle bisectorAn angle bisector is a ray that divides an angle into two congruent angles.JK bisects LJM; thus LJK KJM.
8 Example 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.
9 Check it Out: Example 1mXWZ = 121° and mXWY = 59°. Find mYWZ.
10 Example 2: Finding the Measure of an Angle KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.
11 Example 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.
12 Example 2 ContinuedStep 2 Find mJKM.Substitute 6 for x.Simplify.
13 Check 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.
15 Lesson 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.