chapter 1.4 notes: measure and classify angles goal: you will name, measure, and classify angles
TRANSCRIPT
Chapter 1.4 Notes: Measure and Classify Angles
Goal: You will name, measure, and classify angles.
• An angle consists of two different rays with the same endpoint.
• The rays are the sides of the angle.
• The endpoint is the vertex of the angle.
• Name the angle above: _____, ______, ______• ____________ is the vertex of the angle.
Ex.1: Name the three angles in the diagram.
Ex.2: Name the three angles in the diagram.
M O
N P
• Classifying Angles:• Angles can be classified as acute, right, obtuse, and
straight.
• Acute angles have a measure greater than 0 and less than 90.
• Right angles have a measure of 90. • Obtuse angles have a measure greater than 90 and
less than 180. • Straight angles have a measure of 180.
• Measuring Angles:• A protractor can be used to approximate the measure of an angle.
• An angle is measured in units called degrees (o).
• Postulate 3 Protractor Postulate:Consider and a point A on one side of . The rays of the form can be matched one to one with the real numbers from 0 to 180.
The measure of is equal to the absolute value of the difference between the real numbers for and .
A
O B
OB��������������
OA��������������
AOB
OB�������������� �
OB�������������� �
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EXAMPLE 3 Measure and classify angles
Use the diagram to find the measure of the indicated angle. Then classify the angle.
a. KHJ b. GHK c. GHJ d. GHL
SOLUTION
A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.
• Postulate 4 Angle Addition Postulate:If P is in the interior of , then the measure of
is equal to the sum of the measures of and .
If P is in the interior of , then m RST m RSP m PST
RST
PSTRSPRST
RST
Ex.4: Given that , find and .
145om LKN m LKMm MKN
Ex.5: If find and 72 ,om XYZ m XYW.m ZYW
Ex.6: Given that is a straight angle, find and .
KLMm KLN m NLM
Ex.7: Given that is a right angle, find and .
EFG
m EFH m HFG
• Congruent Angles:• Two angles are congruent angles if they have the
same measure.
Angle measures ar equal Angles are congruent
Ex.8: The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If , what is
?
157om DEG m GKL
Ex.9: Use the diagram below.a. Identify all pairs of congruent angles.b. , , and .
Find the other angle measures in the diagram.
121om TSR 84om QRS 130om PQR
• An angle bisector is a ray that divides an angle into two angles that are congruent.
Ex.10: In the diagram below, bisects , and . Find . m XYZ018m XYW
XYZYW��������������