Transcript 1-3 - White Plains Public Schools

1-3 Measuring and Constructing Angles
Objectives
SWBAT name and classify angles.
SWBAT measure and construct angles and
angle bisectors.
HW 1.3 Page 24 {5,7,9,11,13,17,27,29,31,37}
All problems must have figures redrawn into
HW.
Holt Geometry
1-3 Measuring and Constructing Angles
Vocabulary
angle
vertex
interior of an angle
exterior of an angle
measure
degree
acute angle
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right angle
obtuse angle
straight angle
congruent angles
angle bisector
1-3 Measuring and Constructing Angles
An angle is a formed by two rays, or sides, with a
common endpoint called the vertex (plural:
vertices).
You can name an angle several ways:
1. by its vertex (a single point)
2. by a point on each ray and the vertex (3 points)
3. by a number
Holt Geometry
1-3 Measuring and Constructing Angles
Possible Angle Names:
R, SRT, TRS, or 1
Holt Geometry
1-3 Measuring and Constructing Angles
You can’t name an angle just by its vertex if there
is more than one angle with that vertex.
In this case, you must use all three points to
name the angle, and the middle point is always
the vertex.
Holt Geometry
1-3 Measuring and Constructing Angles
Example 1: Naming Angles
Name three of the angles shown.
Possible answer:
BAC
CAD
BAD
Holt Geometry
1-3 Measuring and Constructing Angles
Check It Out! Example 1
Write the different ways
you can name the angles
in the diagram.
RTQ, T, STR, 1, 2
Holt Geometry
1-3 Measuring and Constructing Angles
The measure of an angle is usually given
in degrees. There are 360° in a circle.
Holt Geometry
1-3 Measuring and Constructing Angles
How do you measure an angle? Use a protractor!
Holt Geometry
1-3 Measuring and Constructing Angles
Holt Geometry
1-3 Measuring and Constructing Angles
Example 2: Measuring and Classifying Angles
Find the measure of each angle. Then classify
each as acute, right, or obtuse.
A. WXV
mWXV = 30°
WXV is acute.
B. ZXW
mZXW = 130° - 30° = 100°
ZXW = is obtuse.
Holt Geometry
1-3 Measuring and Constructing Angles
Congruent angles have the same measure.
mABC = mDEF, therefore ABC  DEF.
This is read as “ABC is congruent to DEF.”
Arc marks are used to show that the two s are .
Holt Geometry
1-3 Measuring and Constructing Angles
Holt Geometry
1-3 Measuring and Constructing Angles
Example 3: Using the Angle Addition Postulate
mDEG = 115°, and mDEF = 48°. Find mFEG
mDEG = mDEF + mFEG  Add. Post.
115 = 48 + mFEG
Substitute the given values.
–48° –48°
67 = mFEG
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Subtract 48 from both sides.
Simplify.
1-3 Measuring and Constructing Angles
An angle bisector is a ray that divides an angle
into two congruent angles.
JK bisects LJM; thus LJK  KJM.
Holt Geometry
1-3 Measuring and Constructing Angles
Example 4: Finding the Measure of an Angle
KM bisects JKL, mJKM = (4x + 6)°, and
mMKL = (7x – 12)°. Find mJKM.
(4x + 6)°
(7x – 12)°
Holt Geometry
1-3 Measuring and Constructing Angles
Check It Out! Example 4b
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
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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
Lesson Quiz: Part I
Classify each angle as acute, right, or obtuse.
1. XTS
acute
2. WTU
right
3. K is in the interior of LMN, mLMK =52°,
and mKMN = 12°. Find mLMN.
64°
Holt Geometry
1-3 Measuring and Constructing Angles
Lesson Quiz: Part II
4. BD bisects ABC, mABD =
, and
mDBC = (y + 4)°. Find mABC.
32°
5. Use a protractor to draw an angle with a
measure of 165°.
Holt Geometry
1-3 Measuring and Constructing Angles
Lesson Quiz: Part III
6. mWYZ = (2x – 5)° and mXYW = (3x + 10)°.
Find the value of x.
35
Holt Geometry
1-3 Measuring and Constructing Angles
Objectives
SWBAT name and classify angles.
SWBAT measure and construct angles and
angle bisectors.
HW 1.3 Page 24 {5,7,9,11,13,17,27,29,31,37}
All problems must have figures redrawn into
HW.
Holt Geometry