Geometry Ch. 5 Test Review

5-1 MidsegmentSolve for x

X=10

X=9 X=7

5-2 Perpendicular Bisector / Angle BisectorSolve for x

X=5X=5/2

5-3 IncenterSolve for x.

Radii of c

ircle

congru

ent X= -1

5-3 Graph the points. Find Circumcenter. Find Orthocenter.

(0,0)(4,-3)

Perp bisectors

altitudes

5-3 & 5-4 Point of ConcurrencyName it!

Altitude

Median Perpendiculuar Bisector

5-3 Draw an angle bisector!

5-3-5-4 Point of ConcurrencyName it!

Angle Bisectors Form _________________Perpendicular Bisectors Form

_____________Medians Form __________________Altitudes Form _________________

incenter circumcente

rcentroidorthocenter

5-3-5-4 Point of ConcurrencyName the line!

5-4 Centroid

5 10

12 36

5-6 List the SIDES in order.Smallest to largest.

54

5-6 Determine the SHORTEST side?

67

47S

M

L

S

M L

Not EG

X

Look for next small

O DG

5-6 Write sides in order from smallest to largest

67

47S

M

L

S

M LXO

DG, ED, EG/ EG, FG, EF

5-6 Longest side of triangle?In triangle ABC,

m<A = 2x + 20, m<B = 4x – 30, m<C = x + 50.Solve for x. Find LONGEST side of triangle ABC.

2x + 20 + 4x – 30 + x + 50 = 180 7x + 40 = 180

7x = 140x = 20

Continuation… Longest side.. In triangle ABC,

m<A = 2x + 20, m<B = 4x – 30, m<C = x + 50.Solve for x. Find LONGEST side of triangle ABC.

m<A = 2(20)+20 = 60m<B = 4(20) – 30 = 50m<C = 20 + 50 = 70

A

C

B60

50

70

AB

5-6 Which lengths could be SIDES of a triangle?

2.5, 8.5, 5.5

6, 5, 11

5x, 8x, 12x

No, 2.5+5.5>8.5 No, 6+5>11

Yes, 5x+8x>12x

5-6 Triangle InequalityFind range of values.

If lengths of sides of a triangle are 2k+3

and 6k, then the third side must be greater than ________ and less than _________

Small side + small side > 3rd side

Small side + small side > 3rd side

2k+3 + 6k > x

8k+3 > x OR2k+3 + x > 6k

-2k -3 -2k -3 x > 4k-3 x < 8k+3

8k+34k-3

Greater thanLess than

5-7 Hinge Theorem & Converse of Hinge TheoremFill in with <, >, or =. By which theorem?

AEB > BDC

so

By Hinge Theorem

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5-7 Hinge Theorem & Converse of Hinge TheoremFill in with <, >, or =. By which theorem?

AB<EDsoBy Converse of Hinge Theorem

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