Geometry
WS 1.2-1.3
Name:_____________________________ Date:_____________ Period:_____
Use the figure below for Exercises 1–8. Note that
pierces the plane at N. It is not coplanar with V.
1. Name two segments shown in the figure.
Possible Answers:
AN , NX , AX , MC , MN , NC
2. What is the intersection of
and
?
Point N
3. Name three collinear points.
Possible Answers: A, N, X
or
M , C ,N
4. What are two other ways to name plane V?
Possible Answers: Plane ANC, Plane ACX, Plane MNX: can’t use R or three points on the same line.
5. Are points R, N, M, and X coplanar?
No: R is above the plane (see directions above)
6. Name two rays shown in the figure.
Possible Answers: AX, AN, NM CM, XA… Remember that you need a
above the name.
7. Name the pair of opposite rays with endpoint N.
Possible Answers: NA and NX or
NM and NC. Remember that you need a above the name.
8. How many lines are shown in the drawing? 3
Algebra Use the diagram at the right for Exercises 28–32.
9. If NO = 17 and NP = 5x − 6, find the value of x. Then find NP and OP.
Since NO = OP (slash marks match)
17 +17 = 34
OP=17
5x-6=34
5x = 40
x=8
NP=34
10. If RO = 6 + x and OQ = 2x + 1, find the value of x. Then find RO, OQ, and RQ.
Single slash marks show that RO = OQ so 6+x=2x+1
x=5
RO and OQ = 11 RQ = 22
Geometry
Name: ______________________ Date: ______________ Period: ______
WS 1.4-1.5
Use the figure at the right for Exercises 1-4. mFXH = 130 and mFXG = 49.
11. Name a pair of vertical angles.
Look for letter x to be formed.
< GXF and IXJ
12. Determine the measures of the missing angles.
mFXH = 130 and mFXG = 49; m<GXH=81, m<HXI=50, m<IXJ=49, m<JXF=131
13. Name a linear pair.
Find three points on a line like F,X, and I then another point off the line like H. Use the letters to name
the angles <FXH and <HXI form a linear pair. Another one would be <GXH and <HXJ
14. Name a pair of adjacent angles that are not a linear Pair.
Adjacent (side by side) that do not form a line. Possible answers include <GXH and <HXI;
<FXG and <GXH; <HXI and <IXJ
15. Algebra If mRZT = 110, mRZS = 3s, and mTZS = 8s, what are mRZS and mTZS?
<RZT is the large angle, <RZS and <TZS are the small angles. Add the two small ones together to get
the big one. 8s+3s = 11s so 11s = 110
s=10 m<RZS=30 and m<SZT=80
16. Algebra mOZP = 4r + 2, mPZQ = 5r  12, and mOZQ = 125. What are mOZP and mPZQ?
<OZQ is the large angle , <OZP and <PZQ are the small angles.
5r – 12
4r+ 2
9r – 10 = 125 9r = 135
r= 15 m<OZP=62 and m<PZQ = 63
Use the diagram below for Exercises 7 and 8. Solve for x. Find the angle. (Fill in diagram)
17. mAOB = 4x  1; mBOC = 2x + 15; mAOC = 8x + 8
<AOC is the large angle , <BOC and <AOB are the small angles.
4x - 1
2x + 15
6x + 14 = 8x+8
x=3
m<AOB=11 and m<BOC = 21
18. mCOD = 8x + 13; mBOC = 3x  10; mBOD = 12x  6
<BOD is the large angle , <COD and <BOC are the small angles.
3x - 10
8x + 13
11x +3 = 12x-6
x=9
m<COD=85 and m<PZQ = 63
19. ABC and EBF are a pair of vertical angles; mABC = 3x + 8 and mEBF = 2x + 48.
What are mABC and mEBF?
a. What does vertical mean (tell you to do with the angles)? Set them equal.
b. Write and solve and equation for x.
3x+8=2x+48 x=40
c. Find the measure of the missing angles. 128 and 128 degrees
20. JKL and MNP are complementary; mJKL = 2x  3 and mMNP = 5x + 2.
What are mJKL and mMNP?
a. What does complementary mean (tell you to do with the angles)? Add up to 90 degrees
b. Write and solve and equation for x.
2x - 3
5x + 2
7x – 1=90
7x=91
x=13 m<JKL=23 and m<MNP = 67
c. Find the measure of the missing angles.
Bisects PQR. Solve for x and find mPQR. (Use for # 11 and 12)
21. mPQS = 3x; mSQR = 5x  20
P
a. Draw and label a diagram. Look right
3x
b. Write and solve an equation for x.
c. Fin the mPQR. 60 degrees
Q
5x-20
3x = 5x-20
-2x=-20
x=10
22. mPQR = 3x  12; mPQS = 30
R
a. Draw and label a diagram. Look right
b. Write and solve an equation for x.
c. Fin the mPQR. 60 degrees
30+30=3x-12
60=3x-12
72=3x x=24
P
30
3x-12
S
Q
R