Pre-CalculusUnit 1 Review Worksheet 1-3

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~--Points, Lines, and PlanesDraw and label a figure for each relationship.

j. Points A, B, C, and Darenoncollinear.

02.. Points A, B, C, and Darenoncoplanar. .

3. Name the intersection of planeABC andHL.

1. Which segments are contained in allthree of the planes GFH, CDl, and ED!?

IIIIII

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II

II

I

IIC IIII

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LG

r: Measuring SegmentsGiven that B is between A and C, find each missing measure.

M

H

5-' AB = 5.3,BC =2,AC = 6.7 b AB = 21,BC = 4.3,AC =2

7~ AB = 3(x + 7),BC = 2(x - 3),AC = 50

A BD '-1. CE \b. BE

I I yII!

C -B -.

ft

A

- - 0 , x- •.

0-..

E

I I !

Refer to the coordinate plane at the right to find eachmeasure. Round your answers to the nearest hundredth..

M tapomt» "flU .,t:!J'IIt:I' I '"'VI '!I' UC:In,c:Refer to the figure below for Exercises 1-~to determinewhether each statement is true or false.

B

S V W RT". -4 -3 -2 -1 0 °1 2 3 4 5 6-6 -5

p

I

3.j

S is the midpoint of TV.' .WR == QV

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V is the midpoint of TW. 7.d.VW<TV

J3: A(4, 2), 2~(-2,10) r~l::: (;. B(-5, 1),M(l, -1)

In the figure at the right, WY bisects UVat Yand UY bisectsTW at X. For each situation, find the value of x and themeasure of the indicated segment.

-7 WX = x + 5, TW = 4x + 5: TX/.8. . UV = x + 6, UY = x-I; YV

B

cA

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Exploring AnglesRefer to the figure at the right to answer each question.

E

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l l. Ifm.LDBF = 35, what is the measure of LEBF?5

\1 N . f!.,9V .•. arne a pair 0 opposite rays.

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\ d. Name a point in the interior of L EBF.

i1.1N h ~I j. ame tree angles with BE as a side? 2

3B F

In the figure, Xii and xi are opposite rays and XCi bisects ,L PXS. For each situation, find the value of x and the measureof the indicated angle.

, ...../l~t mLRXQ = 2x + 7, mLRXP = 3x - 11,

mLPX8 =x + 37; mLQX8 s

f .../ ~j.. mL TX8 = x + 3, mL 8XR = 2x + 9, mL RXP = 4x - 7

mLPX8 p x T

Parallel Lines and TransversalsState the transversal that forms each pair ofangles. Then identify the special name for theangle pair.

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17 L6 and L3; I{ I.

19 L14 and LIO/0·

1/' 9 10 13 14 mJ t~i L7 and LI3 11 12 15 16J I'

8

.>"'t !t.x..:.' .E

Identify all planes that appear parallel to plane FGH, H

') '"c%.{)· Which segments seem parallel to GH?

Angles and Parallel LinesIn the figure, e II m: Find the measure of each angle.1. If mL 7 = 100, find mL3,

2. If mL 7 = 95, find mL6.e

3. If mLl = 120, find mL5.

m4. If mL4 = 20, find mL 7.

5. If mL3 = 140, find mL8.

6. IfmL4 = 30, find mLl.

7. If mL4 = 40, find mL2. 8. IfmL 7 = 125, find mL4.

9. If e .L t, find mL3. 10. If mLl + mL3 = 230, find mL6.

e m

tProving Lines ParallelFor Exercises //-"'l5find the value of x so that ell m:

''}/w;,.,

II.m

r---. Measuring Angles in TrianglesFind the value of x.

(103 - x)O

L) x»,. (6x - 7)0

XO

Exploring Congruent TrianglesLabel the corresponding parts if !::.RST=::: l:.ABC. Use thefigures to complete each statement.1. L C ::::-L S A

2. LR:::: -L

-- ?3, AC=-·R c

-- ?4. ST= -'-

-- ?5. RS=-·

6. LB:::: -L

B

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i· Given 6,ABC ::::l:. DEF, DE = 10, EF = 13, DF = 16, andAC = 4x - 8, findx.

Analyzing Isosceles TrianglesFind the value of x.

1. 2. 3.xo

h xo

"A

600

Find the shortest segment in the figure.

How many of the segments in the figure are longer than BD? c

/

\£) . List the sides of 6MNO in order from longest toshortest ifmLM = 4x + 20, mLN = 2x + 10, andmLO = 3x - 20 ..

The Triangle InequalityDetermine whether it is possible to draw a triangle with sidesof the given measure. Write yes or no.

--J( . 2,3,4

8.9.

8.9, 9.3, 18.3

19, 19,0.5

Determine whether it is possible to have a triangle with the.9 iven vertices. Write yes or no, and explain your answer.

1/\iV, A(3, -6), B(l, 2), C(-2, 10)

I/. A( -4, 2), B( -2, 1), C(2, -1)

rurt» ua .o;,I8I11UQ, In BQDI~'C;~

In the figure at the right, 1::..ABC~ 1::..DEF,BR:::: RC, andES == SF. Find the value of x.1. Be = 24

EF= 15AR =xDS = x - 6

BE

Fc2. AB = 2x + 5

DE =x + 7AR = 24DS = 18

Find the value of x.

3. x

x

9 5

De~ermin.e if the given measures are measures of the sides ofa fight triangle.

!S. 50,75,85

-7{. 45,60,80

300

x4

11\lv' Find the length of a side of a square whose diagonal is 4 em.

Ij. If mL BEA = 135, find mLAED.

c2. IfmLABC = 50, find mLBCD. c·

....1

,c_j. IfAB = 5x - 3 and CD = 2x + 9, findAB.

4. If mL DAC = y and mL BAC = 3x, find x.

5. If AB = X2 - 15 and BC = 2x, find x.

Use rhombus ABCD and the given information to find eachmeasure.

B

6. mLBCE

7. mLBEC

o

RectanglesUse rectangle ABCD and the given information to solve eachproblem.

~. IfAC = 4x - 60 and BD = 30 - x, find BD.

A B

AI":"""----- -::;:oo,B

9. IfAE = 2x + 3 and BE = 12 - x, findBD.

. f)k· IfmLBAC = 3x + 5 and mLACD = 40 - 2x.

FindmLAED.

E

c ~

o c

o

TrapezoidsMATH is an isosceles trapezoid with bases MA and TH. Usethe given information to solve each problem.

r> 1/ If lW.A= 34 and HT = 20, find CD.

I~? If HT = 17.6 and CD = 28.6 find MA. M

i? If mL DCM = 2x, find mL CMA in terms of x.j,j,

1'1. If the measure of the median of an isosceles trapezoid is 5.5,what are the possible integral measures for the bases? l~J -r---::J

A 0 T

J ~)'"I··" f==31A==5Iw=?

2' 4', I

j{o.w = 7, .e = 12 P = ?, -

/) w = 15.5, P = 81, e = ?

Area of ParallelogramsFind the area of each figure or shaded region. Assume that . \ \ \angles that appear to be right are right angles. \V\eN -{\(\C~ .....rfW....~ er', f'fle..:t€/'L .

20 in.

f6.• 5 in.[p4m4m

4m6m

6 in.

10 in.

16 in.

Sm 4m Sm1

\Sm

. 4m

1Sml

11 _

5m 4m Sm

1

\Sm____I

Find the sum of the measures of the interior angles of eachconvex pOlygon.

!J}. octagonr7:2. 13-gon

The number of sides of a regular polygon is given. Find themeasure of an interior and an exterior angle of the polygon.

.., /)C/j· 9 10

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