Transcript 1-5 Angle Relationships
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1-4 HW Answers
12.
Q 21.
Right 13.
P 14.
R 15.
M 16.
TP & PQ 17.
VN & NM 18.
NR & NM 19.
PR & RQ 20.
<4 23.
<8 25.
<4 26.
P,T 27.
Q,S 28.
<9 & <3 29.
<9 & <2 31.
Right 32.
Acute 33.
Acute 34.
Obtuse 35.
Obtuse 36.
Answers will vary 37.
27 39. 16 41. 47
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1-5 Angle Relationships
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Real-Life
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Vocabulary
Adjacent Angles- 2 angles that lie in the same plane and have a common vertex, but no common interior points Linear Pair- a pair of adjacent angles with non-common sides that are opposite rays Vertical Angles- 2 nonadjacent angles formed by 2 intersecting lines – VERTICAL ANGLES ARE CONGRUENT Complementary angles- 2 angles with measures that have a sum of 90 Supplementary angles- 2 angles with measures that have a sum of 180 Perpendicular- lines, segments, or rays that form right angles
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1 2
ADJACENT
3
2 1
4
VERTICAL
<1=<2 , <3=<4 1 2
SUPPLEMENTARY
1 2
LINEAR PAIR
1 2
COMPLEMENTARY PERPENDICULAR
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Examples
1. Name a linear pair
(x-36)+x=180 2x-36=180 2x=216 x=108 (x-36) = 108-36 = 72
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PRACTICE
1. Name a linear pair whose vertex is B
(2x+21)+x=90 3x+21=90 3x=69 x=23 (2x+21) = 2(23)+21= 67 X=23
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Examples
5. If m ∠ RTS = 8x + 18, find the value of x so that TR ⊥ TS.
8x+18 = 90 8x = 72 x = 9 CAN YOU ASSUME?
6. ∠ WZU is a right angle YES Markings tell us so 7. ∠ VZU is adjacent to ∠ YZX.
NO Vertical angles, not adj.
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PRACTICE
5. If m ∠ PTQ = 3y − 10 and m ∠ QTR = y, find the value of y so that ∠ PTR is a right angle.
3y-10 +y = 90 4y -10 = 90 4y = 100 y=25 CAN YOU ASSUME?
6. ∠ NQO and ∠ OQP are complementary.
NO- No right angle markings 7. ∠ SRQ and ∠ QRP is a linear pair.
Yes, straight line
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HW 1-5 Answers
9. < BFC & < DFE 29.
X = 7 11.
< FDG & < GDE 13.
< CBF &
< GDE 17.
< BAD 19.
X = 65 21.
Y = 85 23.
Y =21 , X = 48 25.
< F = 63 , < E = 117 31.
< JNP = 92 35.
A = 8, b = 54 37.
True 39.
can’t determine 41.
False