Transcript Find mJKM. Holt McDougal Geometry 1-3

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..
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Vocabulary
Do you know?
Angle
Measure
Interior of an Angle
Acute Angle
Right Angle
Congruent Angle
Holt McDougal Geometry
Vertex
Degree
Exterior of an Angle
Obtuse Angle
Straight Angle
Angle Bisector
1-3 Measuring and Constructing Angles
Name the Angles
Name each angle in three or more ways.
1.
2.
3. Name three different angles in the figure.
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
mBOA = 40°
BOA is acute.
b. DOB
mDOB = 125°
DOB is obtuse.
c. EOC
mEOC = 105°
EOC is obtuse.
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.”
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
angle bisector
An angle bisector is a ray that divides an angle
into two congruent angles.
JK bisects LJM; thus LJK  KJM.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
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.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Check it Out: Example 1
mXWZ = 121° and mXWY = 59°. Find mYWZ.
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.
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.
Holt McDougal Geometry
1-3 Measuring and Constructing Angles
Example 2 Continued
Step 2 Find mJKM.
Substitute 6 for x.
Simplify.
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.
Step 1 Find x.
LJK = KJM
(–10x + 3)° = (–x + 21)°
+x
+x
–9x + 3 = 21
–3
–3
–9x = 18
x = –2
Holt McDougal Geometry
Def. of  bisector
Substitute the given values.
Add x to both sides.
Simplify.
Subtract 3 from both sides.
Divide both sides by –9.
Simplify.
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) + 21 Substitute –2 for x.
= 20 + 3 + 2 + 21
= 46°
Holt McDougal Geometry
Simplify.
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
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Homework:
1.3 Handout – will be given out once textbook work is
checked.
Holt McDougal Geometry