Name

Benchmork Test 3

If you know that DEll AC, and that D andEare midpoints, which of the followingguarantees that,{C : 2DE!

Midsegment TheoremAltitude Theorem

C CPCTCD Definition of triangle bisector

Class

3. Find the value of x.

Date

Find the measure of angleMNQ.

2y- 4

y+3

A3

DT2

4. gÚ, RW, and fr aremedians. Findthelength of XT.

s

F 60"B0'

H 100"J LzO"

Ltl-4 =

I --'1

1r3

F9 H 16GI4 IB

5. \,Vhat is the point of concurrency of thealtitudes of a triangle?

A circumcenternterocenter

D centroid

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Name

6. Which of the following can be used toinscribe a circle in a triangle?

circumcenterincenter

H orthocenterJ centroid

7. What is the center of a circlecircumscribed about a triangle withvertices (-2,2) (2,

,2),0)

c (0,2)D (0,0)

Class

9. Given: Unes ræ andnintersect atpointP.Prove: Lines ru and,nare coplanar.Which of the following could be a

vr'r,

8. Suppose you are asked to complete thefollowing indirect proof.Glven: nis negative.Prove: n2 is positive.Which of the following is the assumptioninthei tproofl

is positive.2 is negative.is any real number.

J r¡ is neither positive nor negative.

statement in the T9ueclproof?A Lines m and n do not intersect at

P,

mandn are not coplanarwithP,

C Since lines m and n are not in thesame plane, they do not sharecommonpoints.

D Since lines nr and z do not sharecommon points, they are notcoplanar.

10. Glven: AABCis an isosceles triangle andrnLA-- 90'.

Prove: ¿.4 is the vertex angle.Which of the following could be astatement in the indirect proof?

= LB,then* mt-B I mLC: IB0o.

(t,,,

þ,-z)

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11. In a field, Raja, Mary, and Miguel arestanding in the shape of a triangle.Raja is l2B feet from Mary and Maryis 143 feetfrom Miguel. Which of the

,*

following is a possible dist e betweenRaja and Miguel?

S3feet ,Lt/\^C-288ftetDie:Ffieer flr*

12. On a map, Meridian, Birmingham,and Montgomeryform a triangle.

Class

\01qì"6rO\'ort'4

Meridian is 109 miles from Birminghamand Birmingham is 9t miles fromMontgomery. Whichof the followingis not apossible distance betweenMontgomery and Meridian?

&t

14. What is the sum of the measures of theinterior angles of the figure below?

N

l,{ 3

Date

F 900'G 720"

00

J 360"

1 5. The measure of each interior angle of atgþr I2-sidedpolygonis ?

4Bo Qz-z),tto50' Ic 152'D IBo" ø 15ô

1 6. Figure ABCDEF is a regular hexagon.\tVhat is the measure of LEFG?

CD13. 4 and 7 represent the lengths of the sidesof a triangle. Give all possible lengths forthe third side if the lengths of the sidesare all integers.

o (s-z) - tto

,7,8,9, r0, ll, 123, 4, 5, 6,7 ,8,6,7 r8,516,7, Br g, I0

: 5'lo

ALl

3 L x ¿ ll

4 t?: lf

1-'l' 3

0o

00

H 90'I 120"

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(c -z),1ñ = 7zÔ

Ç= no

Use the given coordinates to prove themost precise name for each quadrilateral.

ra. q(r,r), u\2,-q),a(-a,-a), o(-+,2)

Name

A?t,4)

(r,rì F Parallelogram@' uare

- omb:1 J rectangle

t-ttt ,r,j,

Class

20. Which of the following would prove thatquadrilateral QRSTis a parallelogram?

OR

ombus 6.0 = ffi

ß. q4,-3), o(0,-s), r(-a,r), ¡(r,s)A parallelogram

es

p4=l;í

F QR=STG aRllsr

Fand7F^=pnairs of sides are congruent.

21. In LTHI, M and D are midpoints of/T and F, respectively. Which can beproven true?

r

( (t'3\

(,

(,.at

D @rtl

) (.tLt

ù{

.3)I

sure of angle T is equal to theof angle R.

/r\-c rM: \.r/rO n=ln

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22. Which additional piece of informationwould prove that quadrilateral WXYZshown below is a parallelogram?

=AYc -VVZ =Ñ

H LWAX = LZAYI wLWAX * nLYAX:LB}

23. The values for which ordered pair willshowthat MATH is aparallelogram?

Class

24. Use the given coordinates to classisrthe triangle and find its perimeter P.s( r, -o), a(0, -o), u(s,-z)

cuteisosceles; P : 15cuteisosceles; P : l0 + 2\/lcutescaleneiP: lO + 2\/i

J acute scalene; P : 15

25. Arcs of congruent circles wereconstructed from the endpoints of fr,intersecting atpoints á and B as shown.Whatis true about anypoint P on Æ inthis construction?

Date

^ (-''i)e (r,r),-7),-2)

Vx-8 = 3Y+to5x-z =il-Y

A APXfwillbe an acute isoscelestriangle.

26. Which of the following statements isNOT true?

F The diagonals of a rhombus a¡eperpendicular to each other.

G The diagonals of a kite areto each other.of a kite bisect

each other.J The diagonals of a parallelogram

bisect each other.

( r'o

tlx = 51¡ --3

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27.I}:e coordinates of three vertices of aparallelogram are (0, 0), (8, 5), and (fS, z).Which of the following is not apossiblefourth vertex?

7,2) (o,r]_

The figure shown is a kite. What is thex-coordinate of point P?

. ú (5,t)(oíl i-.

Class

29. Find the midpoint of the midsegment ofthe trapezoid if.A : (4s,4t),B : (4u, 4t), andç = (4u,0).

Date

t ls r4r

a.F -+42a*4G-

2+2

I 2a*4

t*u*u,t)s * u * u,Zt)

C (u + 2u,2t)D (2s * 2u,2t * 2t)

B tlo ,4t('+,(qV, o)

30. Quadrilateral JI(LM has verticesI(-4, -r),K-1, 2), andL(6,2). Forwhat coordinates of point M is JKLM a

,"+)

parallelogram?

3, -2)3, -l)

H (4,0)t (4, -t)

N (zu +2v ,Lt)n (zs) Lt)

ç(-l'¿)

X (s+,., av ,2t)

5({, -r)

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L ( ç,r)