1.6-1.7 Angles and Their Measures
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Transcript of 1.6-1.7 Angles and Their Measures
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1.6-1.7 Angles and Their Measures
Geometry
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Objectives:• Use angle postulates• Classify angles as acute, right, obtuse, or
straight.
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Using Angle Postulates
• An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex of the angle.
• The angle that has sides AB and AC is denoted by BAC, CAB, A. The point A is the vertex of the angle.
sides
vertex
C
AB
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Ex.1: Naming Angles
• Name the angles in the figure:
SOLUTION:There are three different
angles.• PQS or SQP• SQR or RQS• PQR or RQP
Q
P
S
R
You should not name any of these angles as Q because all three angles have Q as their vertex. The name Q would not distinguish one angle from the others.
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more . . .
• Angles that have the same measure are called congruent angles.
D
EF
50°
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Note – Geometry doesn’t use equal signs like Algebra
MEASURES ARE EQUAL
mBAC = mDEF
ANGLES ARE CONGRUENT
BAC DEF
“is equal to” “is congruent to”
Note that there is an m in front when you say equal to; whereas the congruency symbol ; you would say congruent to. (no m’s in front of the angle symbols).
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A
D
E
Interior/Exterior
• A point is in the interior of an angle if it is between points that lie on each side of the angle.
• A point is in the exterior of an angle if it is not on the angle or in its interior.
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Postulate 4: Angle Addition Postulate
• If P is in the interior of RST, then
mRSP + mPST = mRST
R
S
T
P
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Classifying Angles• All angles are classified as acute, right, obtuse, and
straight, according to their measures.
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6 and 5 are also a linear pair
m5 = 50˚.
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