Download Section 1-3 Measuring and Constructing Angles

CHAPTER 1
1-3 MEASURING AND CONSTRUCTING ANGLES
DEFINITIONS
• What is an angle?
• It is a figure formed by two rays, or sides, with a
common endpoint called the vertex (plural:
vertices).
How can we name an angle?
You can name an angle several ways: by its vertex,
by a point on each ray and the vertex, or by a
number.
HOW TO NAME AN ANGLE
• The set of all points between the sides of the
angle is the interior of an angle. The exterior
of an angle is the set of all points outside the
angle.
• Examples of naming angles can be:
Angle Name
R, SRT, TRS, or 1
EXAMPLE 1
• A surveyor recorded the angles formed by a
transit (point A) and three distant points, B,
C, and D. Name three of the angles.
• Answer:BAC, CAD, BAD
EXAMPLE 2
Name the following angles in three different ways
1-3 MEASURING AND CONSTRUCTING
ANGLES
USING A PROTRACTOR
• You can use the Protractor Postulate to help you
classify angles by their measure. The measure of
an angle is the absolute value of the difference of
the real numbers that the rays correspond with
on a protractor.
• If OC corresponds with c and OD corresponds
with d,
• mDOC = |d – c| or |c – d|.
EXAMPLE 3
• Find the measure of each angle. Then
classify each as acute, right, or obtuse.
• A. WXV
• mWXV =180-150= 30°
• WXV is acute.
B. ZXW
mZXW = |130° - 30°| = 100
ZXW = is obtuse
EXAMPLE 4
• What are congruent angles?
Congruent angles are angles that have the
same measure. In the diagram, mABC =
mDEF, so you can write ABC  DEF. This is
read as “angle ABC is congruent to angle DEF.”
Arc marks are used to show that the two angles
are congruent.
ANGLE ADDITION POSTULATE
EXAMPLE 5
What is m<TSW if m<RST = 50 and m<RSW = 125?
T
x
W
50
R
S
Step 1: Set up an equation
RST  TSW  RSW
Step 2: Plug in the given information
Step 3: Solve for the missing variable.
50  x  125
x  75
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EXAMPLE 6
• T is in the interior of
RSU . Find the following:
• A) mRSU if mRST is 12 and mTSU is14.5
• B)
mRST ifmTSU is 10.3 and mRSU is 65
ANGLE BISECTOR
• What is an angle bisector ?
• An angle bisector is a ray that divides an angle
into two congruent angles.
• JK bisects LJM; thus LJK  KJM.
Example 7: Finding the Measure of an Angle
KM bisects JKL, mJKM = (4x + 6)°, and
mMKL = (7x – 12)°. Find mJKM.
Example 7 Continued
Step 1 Find x.
mJKM = mMKL
Def. of  bisector
(4x + 6)° = (7x – 12)°
+12
+12
Substitute the given values.
Add 12 to both sides.
4x + 18
–4x
= 7x
–4x
18 = 3x
6=x
Simplify.
Subtract 4x from both sides.
Divide both sides by 3.
Simplify.
Example 7 Continued
Step 2 Find mJKM.
mJKM = 4x + 6
= 4(6) + 6
Substitute 6 for x.
= 30
Simplify.
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