Test Review: Geometry IPeriod 5,7

ASSESSMENT DATE:

Period 1: Friday February 10.Period 5/7: Monday February 13.

Things it would be a good idea to know:

1) Polygonsa. Names by number of sidesb. Difference between concave and convexc. Difference between regular, equilateral, equiangular

2) Quadrilateralsa. Properties of parallelogramsb. Properties of special parallelogramsc. Properties of Trapezoids, Isosceles trapezoids, Kites

3) How to prove a quadrilateral is a parallelogram on a coordinate plane or in a two-columnproof

4) How to prove a quadrilateral is a trapezoid or an isotrap on a coordinate plane.5) How to find lengths of segments and measures of angles using the properties6) How to use algebra to find measure of angles and lengths of sides

Test OutlinePart I: 5 multiple choice, 5 true false (lopts)Part II: 9 problems (90 pts)

Practice problems attached.

Name:

S

S

Definitions; YOU NEED TO KNOW THESE!!!

Rhombus:

Period: _____ Date:

Rectangle:

Square: —

Decide whether the statement is always, sometimes,or never true. Draw examples!!

a) A rhombus is a rectangle

Review: What features do all parallelograms have?

6.4 Special Parallelograms

b) A parallelogram is a rectangle

Diagonals of Special Parallelograms

What we already know about diagonals of parallelograms:

Diagonals of a Rectangle are... :>~~:Biconditional Statement:

Diagonals of a Rombus are...

Biconditional Statement:

Diagonals of a Square are... M~i.

Biconditional Statement:

**Alj properties of parallelograms are ALSO true for rectangles, rhombU, and square...because theyARE PARALLELOGRAMS!**

1) ABCD is a rectangle. What else do you know about ABCD?

A S

LZ~2) In the diagram,

P

27+

PQRS is a rhombus. What is the value of y?

What property of rhombi will you use?

Equation:

Solve

3) What is another name for an equilateral quadrilateral? ______________________________________

4) Decide whether the statement is sometimes, always, or never true.

a. A rectangle is a parallelogram.

b. A rectangle is a rhombus._____________________

c. A parallelogram is a rhombus. __________________

d. A square is a rectangle.

5) Which of the following quadrilaterals have the given property? Only one answer for each!

All sides are congruent a) Parallelogram

All angles are congruent b) Rectangle

The diagonals are congruent c) Rhombus

Opposite angles are congruent d) Square

6) MNPQ is a rectangle. What is the value of x?

M Pd2k

U P

S R

NAME DATE _____________

Chapter Test AFor use after Clmpter 6

What special type of quadrilateral is shown?

Tell whether the polygon is best described as equiangulatequilateral, regular, or none of thesa24. 25. 26.

un Geometrya Chaybor 6 Resarce

Copyright © McDougal Liltell Inc.All rights reserved.

21.21.

(22.

23.

24.

25.

26.

27

28.

29.

30.

31.

7~

3 in.

32. See loft.

33. Soc loft,

34. See left.

35. See loft. C

D w a figure that fits the descrjp3J~n. Do tH~St~,

n equilateral pentagon equiangular quadrilateral

regular hexagon ~~2oncave quadrilateral

(

1

1.

2.

3.

4.

5.

8.

7.

Copyright® McOougal LitelI Inc.All rights r~soni~d.

Geometry (~~]Ch4xe, 8 Resc.sr~~

OAK

Chapter Test BFarunaft.Chaptsg

Decide whether the figure Is a polygon.

tJJ afl\i~

State whethe, the figure is convex or concava

~~0 _ 8.

4.5

VDecide whether the statement isnever true.9. A rhombus is a square.

10. A rectangle is a parallelogram.

11. A trapezoid isa parallelogram.

12. A parallelogmm is a rectangle.

Find the values of z

) 13. X_15~1E~1iX

always, sometimes, or

~3x~

72°\

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19,

20,

— 5)0

15.

Oecid~ if you are given enough information to Prove that thequadrilatera’ is~ a parallelogram.

17. One pair of opposite sides are congruent.

18. Two pairs of opposite angles are congruent,

19. All pairs of consecutive angles are congruent.

20. Diagonals are perpendicular

(Sx + 29J

)

NAME DATE

Chapter Test BFor usa ~ftsr Chegsr 6

What special type of quadrilateral is shown?

21. L 22. 23.

25. 26.

Find the area of the,,quadrllateral.

7 cm

3.5 cm 3.5 cm

7 cm

fr’2m

9m 9m

12 rn

regular quadrilateral

F” GeometryCapyri~ht ® McDoogal Liftell Inc.

All tights reserved.

\ II~

I

Tell whether the polygon is best described as equlangular,equilateral, regular, or none of thesa

25.

26.

27.

28.

27.0

29.

30,

31

32. See left.

33. See left.

34~ See left.

35. See left

II

Draw a figure that fits the

equilateral quadrilateral

description. ‘Do

y4arie~uiansuiar pentagon

concave hexagon

0~>lw 6 Resc,,xce Soak

I

r _

Decide whether the figure is a polygon.

L<EEED>2L_C3EZEE~State whether the figure is convex or concava

Decide whether the statement is always, sometimes, ornever true.

9. A rhombus is a quadrilateral.

10. A rectangle is a trapezoid.

11. A trapezoid is an isosceles trapezoid.

12. A parallelogram is a rectangle.

Find the values of x.

+ 15 14. r7T~2x+2J

15. 16.

Decide if you are given enough information to prove thatthe quadrilateral is a parallelogram.

17. One angle is a right angle

18. 1\vo pairs of opposite sides are congruent.

19. One pair of consecutive angles are congruent.

20. Diagonals are perpendicular and congruent.

21. Opposite sides are parallel and congruent.

22. MI four sides are congruent.

CopyiiQl4i~ Mc000cai Utto~ bc.All riqtds regvvod.

NAME OATh ________

Chapter Test CFGr ms efter Cbapts S

1~.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

is.

16.

17.

18.

19.

20.

21.

22.

GeometryChEpra 6 Rosctat~ Scok

a figure that fits the given,despription. t>a tuEsE (equiangular quadrilateral 7’ ~“~h equilateral pentagon

at is not equiangular

31. _________

32. __________

33. __________

34. See loft.

35. See loft.

36. See left.

decagon (5~~nonconvex quadrilateral

Copyright © McDougal hobO Inc.All rights resarvod.

CHAPTERNAME ________________________

6 Chapter Test CC0NTINUEDI___________ For use altar ChaptarS

What special type of quadrilateral is shown?

DATE

234~ ~ 2t\ç_3 25~

Tell whether the polygon is best describedequilateral, regular, or none of thesa

26.Qas equiangular.

23.

24.

25.

26.

27.

28.

29.

30.28T~ )29.\2

/

C

C6.5 m

37. See left.

GeometryO-i~,ia 6 Rasa.rco Bock

NAME

SAT/~~ DATEChapter TestFoe no after Cbs pint S

(t©©(0

4. What ase the values of the variables in quadrilateral MNOfl

15y+ 16)°

5. NPQR is a trapezoid and ST = 24. Find thevalue of .r.

N~5~

2x — S

® 48 square units (A)© 6Osquare units (D)

(ED~ 70 square units

(~ Only one pair of Opposite angles arecongruent

<1) Opposite sides are congruent.

(C) Diagonals bisect each other.

(~) Diagonals are congruent

‘.0 None of these are true.

8. What special type of quadri1a~er~ has thevertices F(—6, —2), Gfl, —2), H(— 6, —5),and 1(1, —5)7

1. In quadriIater~ 48Cr), Afl ~V and LA andLB are supplementsry Which statements aretrue?

1. Quadrijat~~ ABCD is regular.

ft. QuacJrjjate~j ABCD is a rectangle.

HI. Quadrilateral 48Cr) is a rhombus.

I only

II. UT only

none of these

1. H only

I, II, and Ill

,a3

KC) 8

~0 ii

j

Find the area of a triangle with vertices(0, 2), 8(8, 2), and C(4, —3).

CA) 17 (B) 20 (C) Is

(Ø~ 19 t~ 18

3. Find the value ofx.

(Sx +

Find the area of a parallelogrwn with verticesA(—4, 2), 8(1,6), C(,15, 6), and 13(10, 2).

56 square units

5! square units

7. Choose the statement that is true about a kite.

0

& x4,yztj9

(C) X5,y27j) x=7,y2o

Copyright c~i McOauQai t~ttolf Inc.A~ ogffis rosoniod.

Cx— 8}~ 21

25

28

31

34

9.

— 15)’

©rectangle

parallelogram

kite(a

square

rhombus

“B)

‘~~) X3,y3~

)

DEFG is a trapezoid and H! 15,5. Find theValue oCx.

o jx+3

2x—12

.4)13

‘3 12

P a) 14

t~ 16

Geometry rrnCh~ia~e Ro0n~ Bock

Use the information in the diagram to solve for x. Diagrams may not bedrawn to scale.

1. (1 2. — 69°

Lx2 + 29°

3. 4. (100 — 39°

(80 — 49°

(120 + 29°

(60 + 59’

Use the information in the diagram to solve for x and y.5. 6.

4’

Use the diagram to find the sum of the interior angles in the polygon.7. Pentagoi~ 8. Hexagon 9. Octagon

Tell whether the statement is true or false. If it is false, sketch acounterexample.10. Every equiangular polygon is convex.

11. Every equilateral polygon is convex.

4,Copyright© McDougal LItteIt Inc.Alt rights reserved.

NAME ~-. DATE

Challenge: Skills and ApplicationsFor use with pages 322—328

Goomotj-y~ Resource Book

NAME .___ ____________________________________________ DATE

Challenge: Skills and Applications________________ For use with pages 330—337

In Exercises 1—5, assume PORS is a parallelogram.

1. If PQ = — 10 and SR = it, find all possible values ofx.

2. If PQ = 9 — x~ and QR = x + 2, find all possible values of x.

3. If mLP = (x2)° and rnLQ 1 lx°, find all possible values of x.

4. If tnLQ = 5.?, mLR = (it — 2y)°, and rnLS = (it + 5y)°, find all possible values of xandy.

5. If rnLP = (8y + 2)°, mLR = (y2 — I 8)°, and rnLS = (2x2)°, find all possible values of x andy.

6. Refer to the diagram. Write a two-column proof.

Given: JJKL is a parallelogram whosediagonals intersect at 0.

Prove: 0 is the midpoint of MN.

7. Refer to the diagram. Write a two-column proof.

Given: .4BCD and EFGH are parallelograms.

Prove: AFAE LiHCQ

LESSON

6~2

J

B

D

Two sides of a parallelogram are shown.Use a compass and straightedge to constructthe remaining two sides.

Copyright ~) McDougal Uttell Inc.A~I rights rosorved.

4,

GeometrycThapter 6 Reso.soe Book

I I

NAME___________________________ DAm

Challenge: Skills and ApplicationsForusewitnpagn3s6...3~~

lii Exercises i—3, each figure shown is a trapezoid with its midsegmentFind all possible values of x. Diagrams may not be drawn to scale.

2.

In Exercises 4—5, write a paragraph proof.

Prove Theorem 6.15: If a trapezoid has a pair of con~entbase angles, then it is an isosce1e~ trapezoid.

Given: ABC’D is a trapezoid,AB JJ DC, and LD LC

Prove: ABCD is an isosceles trapezoid,

(Hint: Draw an additional line segment.)

K Given: PR ± ~, P~’Q PS,T is not the midpoint of PR.

Prove: PQRS is a kite.

SIn Exercises 6—B, the coordinates of three vertices of an isosceles trapezoidare given. What are the coordinates of the remaining vertex? (Find ordescribe all possible answers,)

6. (0, 0), (2, 2), (4, 2)7. (0. 0), (26, 0), (0, 39)

8. (—5, 10), (0, 0), (5, 10)

GeometryCh~3i~- 6 Resounte Sook Copyright © MeDougel Littell Inc.

All ñghts reserved,

~

I1. 8—x

2x 3. 16

— 2

LI ‘‘I;I

1:

0 C

AP

Geometry NAME:

WORKSJJEET~ Testsfor Parallelograms PERIOD: _______ DATh:

3) Will this always form a parallelogram?o Yes o No (provide a counterexample)

5) Will this always form a parallelogram?o Yes o No (provide a counterexample)

2) Will this always form a parallelogram?o Yes o No (provide a counterexample)

/4) Will this always form a parallelogram?

o Yes o No (provide a counterexample)

Q ti

6) Will this always form a parallelogram?o Yes o No (provide a counterexample)

Tests for Parallelograms

A Parallelogram is defined as a quadrilateral with both pairs of opposite sides paralleL

Does the given information make the QUADRILATERAL a PARALLELOGRAM?If the information does not guarantee a parallelogram, sketch a counterexample that demonsiratesanother possible shape having the same characteristics.

1) Will this always form a parallelogram?o Yes o No (provide a counterexampIe~

Q U Q U

D A D A

7) Will this always form a parallelogram?ci Yes ci No (provide a counterexample)

9) Will this always form a parallelogram?aYes ci No (provide a counterexample)

11) Will this always form a parallelogram?ci Yes a No (provide a counterexample)

13) Will this always form a paraUelogram?ci Yes ci No (provide a counterexaznple)

Q U

8) Will this always form a parallelogram?ci Yes ci No (provide a counterexample)

D~ fri /U

10) Will this always form a parallelogram?ci Yes ci No (provide a counterexaniple)

7’12) Will this always form a parallelogram?

ci Yes ci No (provide a countetexample)

Q U

14) Given: QUAD is a parallelogramProve: AQDA~LAUQ

U

D p.

U

7U

A

D A

L /D

Tests for Parallelograms

We can test ifa quadrilateral is a parallelogram jf itpossesses certain properties.

Complete thefollowing:

A quadrilateral is a parallelogram if...

I) Both pairs of opposite sides are _____________________

2) Both pairs of opposite sides are _____________________

3) Both pairs of opposite angles are _____________________

4) One pair of opposite sides is both ___________________ and ____________

5) Consecutive angles are __________________________

6) The diagonals ____________________ each other.

7) A diagonal of a parallelogram will always divide the parallelogram into

two _______________________________

These tests describe properties ofALL parallelograms. In certain parallelograms, we find evenmore specific properties.., these parallelograms are called Special Parallelograms.

SPECIAL PARALLELOGRAMS... A Rectangle, Rhombus, and Square have all the propertiesdescribed above, but other properties make them special.

What is the name ofthe parallelogram where...

1) All angles are right angles: ________________

2) All sides are congruent: ______________

3) Diagonals are congruent:

4) Diagonals are perpendicular:

5) Diagonals bisect both pairs of opposite angles:

Geometry

WORKSHEET: Special Parallelograms

NAME: ______________

PERIOD: DATE:

A Rhombus is a parallelogram with...

A Rectangle is a parallelogram with...

A Square is a parallelogram with...

Use the Veini Diagram below to answer the questions thatfollow.

TRUE or FALSE.

1) _____ All rectangles are squares.

3) _____ All squares are rectangles.

5) _____ All rhombi are squares.

7) _____ Some rectangles are rhombi.

Complete thefollowing.

9) A rhombus can be a rectangle if it is

____ A rectangle can be a square.

____ A rhombus can be a square.

Every square is also a rhombus.

____ All rectangles are rhombi.

Special Parallelograms

Parallekgramc

2)

4)

6)

8)

10) A rectangle can be a rhombus if it is

Name

PropertieS of Rectang~es ar~d Sq uares

name of each figure

Parallelogram Rhombus Rectangle Square

1. The diagànals are perpendicular.

2. The figure has four right angles.

3. Th& opposite sides are conguent. I4. The diagonals are con~uent.

5. The figure has four congruent sides.

[ 6. The diagonals bisect each other. j7. Tbe consecudve angles are supplementty.

8. Each diagonal bisects a pair of opposite angles.

9. The figure has exacUy four ~es of symrne~~. —

10. The figure is a rectangle.

ABC’D is a rectangle, with AC = 18. Find each length or angle measure. ‘ A B

U. rnZBCD 12; mZl 13. ,nfl —

14. rnZ3 15. mZ4 16. rnLS —

17. mZ6.,,,,,~ 18.AS 19. DB,.....~

GHKL is a rectangle that is not a square. Answer true or false.

20. GHKL and its diagonals form four congruent triangles.

zi, eua and its diagonals form four isosceles triangles.

22.Ll~Z2 . L

23.LaGHLaAKLH -

24 ~K is a line of symmetry.

2.5. 1≥~GML E AJ-IMK

26.~7?ERL

D C

H

lk

/5

Date

Complete the table. Place a check rurk under thefor which the property is always true.

C,

C,

C

-Name ____________________________________________________________Date

~ncEr.

Properties of kbo~b~se~ - (_- - -.

Trite or false? . -

1. Eve~ rhombus 15 a pa~1leiocarn._

2. The diagonals of a rhombus bisect each other.

3. The diagonals of a rhombus are congruent

4. The diagonals of a thombus a~ pe~endic~~ to each other~

5. The consecutive angles of a rhombus axe conaruent ___..........._—

6. The cousecutive sides of a rhombus are con~jent --

7. A rhombus and one of its diagonals form two isosceles niangles. Z...._____—

S. MNPQ is a rhombus. Find the measure of 9. GHJK is a rhombus, -with GJ = 42. Findeach angle. the length of each segment.

ml 1 — mLW~6Q_ GM—

mZMNP— m12— Li —

rn14 -

10. ABCD is a rhombus. Find each angle measure or segment length.

naIl _________ mLD~ S C

nil2 ___— m13

nil4_A D

BD _ ED

II. EFOM is a rhombus, with ynLEFO = (3x -. 15)D and

m/-EKF = (2x - 3Q)~FindxandrnLEFG.~_— I,

i~1

HJ_

Lff..~__

Rhombus & Factoring Practice

1) Given Rhombus ABCL) whose diagonals intersect at B.AB7x2±28BC = ± 31x

mZBCA2w~-l8wmLDBA3w+63

BE=y~-~yDB 17y- 15

Find w, x, & y

2) Solve the following systems:

3x2—4x—20 6x2—llx—12

8x2—26x+l5 2x2±x—36

3) Solve the following questions given Rhombus USCG whose diagonals intersect at A.a. If rnZUSA = 44° find mZCGAb. If mZGUS = 102° find rnZACGc. IfUCIS fmdSGd. IfUClOfmdACe. If mZSGU = 12° find mLSCGf. If mZUSC 81° find mZUAS

/