geometry: semester i exam study guide #l multiple...

Geometry: Semester I Exam Study Guide#l - 67 Multiple Choicet+68 76 Free Rcsponse

Vocabulary:

Complementary AnglesSupplementary AnglesSkew LinesParallel LinesPerpendicular I-inesSegment BisectorEuclid's Undefi ned TermsTheoremPostulateAxiomFlypothesisConclusionNegationCongruentRegular

Questions (1 pt each)(4 pts cach)

Theo rem s/Postulates/Prope rties :

Segment Addition PostulateAngle Addition PostulateParallel Line Theorems and their Converses

Ex: Corresponding angles = if parallel lines are cut by a transversalConverse: Lines are parallel il'corresponding angles =

Reflexive PropertyTransitive PropertySymmetric PropertyDistributive PropertyAddition/Subtraction/Multiplication/Division PropertiesSubstitution Property5 Theorems for proving triangles congruent (SSS, SAS, ASA, AAS, HL)If two angles are congruent in a triangle, opposite sides are congruent (also know the converse)

Skills:

Find midpointWrite converse of a given conditional statementFind sum of the interior angles of convex polygonsFind measures of exterior angles of convex regular polygonsFind missing measures of trianglesFind missing measures given parallel lines cut by a transversalFind perimeter and area of triangle, square, rectangle, circle, etc.Find the surface area and volume of a prismComplete a proof using parallel lines and congruent triangles

EquilateralEquiangularPolygon Names: (3 - l2 sided)Ex: Triangle, Quadriìateral, .

DistanceEquid istantMidpointPerpendicu lar BisectorMedianAltitudeAngle BisectorMidsegmentAcute TriangleObtuse TriangleEquilateral Triangle

Right TriangleIsosceles TriangleScalene TriangleVertical AnglesCorrespond ing AnglesA lternate Interior AnglesAlternate Exterior AnglesConsecutive lnterior AnglesLinear PairCo llinearCoplanarBetweenParallelogram

CEOMETRY

Revìew for First Semester Exam

Determine if each statement is true or false.

/ T I F l. The negation of "Our test is on Monday" is "Our test is not on Monday."/ -\.ì

T F 2. If a conditional statement is true, its converse is also true.

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. \ \/(e) 4. If twolinesarecutbyatransversal,thecorrespondinganglesarecongruent.

F 5. The median of a triangle is a line segment that goes from a vertex of the triangleto the midpoint of the opposite side.

F 6, Every triangle has three medians.

(pt. L Medians and altitudes are the same thing,

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T

TI

T

F' 8.

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The altitude of a triangle is also called the height.

If two sides of one triangle are congruent to sides of another triangle, the thirdsides are also congruent.

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10. Iftwo lines do notintersect,then they areparallel. f ¡ n't^"' "'')

I l. A statement that is accepted without proof is a postulate.

F12F13Ft4

. A and B are collinear.

. E, F, and G are coplanar.

. B, C, and D are coplanar.

. B, C, D, and G are coplanar..

. All the points are coplanar.+> +>. BD and DB are the same.

-+ ->. GH ancl HG are the same.

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19. lf m1l = 105o, then ml3 --

2A. ff mZ2 = 100o, then mZ4 =

2l. lf mZ3 = 115o, then mZ2 =

22. If mZl - 100", then ml5 =

iA,'

Determine if each of the following triangles is congruent. If they are congruent, tell whichtheorem or postulate you would use to prove them congruent.$

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23. a

M

tn lln

27. 7'/'')I

26.

28.

Solve for each variable.

3x+15 'l

29. x=

t/'l,il

31. x=

30. x=

y=

y=

33. x=

l(. 32. x=

y=

t' '

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35. x= 36. x=

37. For A(-2,4) and B(1, l), find

a) the slope of AB I - 'lé

o,ñWf+(r -tS,

c) the midpoint of AB-L+ I

2-

<>d) the equation of AB

=-*--m

e) the slope of a line perpendicular to AB

38. which lines, if any, can be proved parallel from the given information.

Y -- -/x +f| __ _¡(t) +L

l= -l rb'z--b

a) Zl=22 /A/oAab) 22 = 23 tVotec) Z2= 24 ill Kvrd)

e)

Ð

s)

h)

i)

zt=26 jlt"[z4= 25 \il!mz2+mZ3=t$o" t/lKmZ3 + mZ4 = l8O" Notle-nLj nlk j(lKiilk kilr \jll/

41. Given: BC bisects ZDBE

Prove: ZABD = IABE

+

-+BC bisects ZDBE

ZABD and ZDBC are a linear pair

ZABD and ZDBC are supplementaryZABEand ZEBC are supplementary

ZDBC= ZEBC

ZABD = ZABE

2. D.{nnr+h/,^ oI LMe^r Par

C>¡ur^

3. l)'neX

4.

5.

D "{¡niftoa

?o.Ns ^fs t't*'n\"f

of 8,s"fy's o..te ;) f/'qn

suælen',cnb a'rs 2lr

42. Given: C is the midpoint of BD

ncjgDProve: ZB = lD

Statements

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Bc

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3 . D.{m¡l,on

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