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Ch 5 Review Game & Answers
RS || _____
If TY = 4, then RS = _____
ST || _____
If RT = 7, then XY = _____
Use ∆WXY, where R, S, and T are midpoints of the sides.
X
YW T
RS
What are TR, RS, and ST called?
Ch 5 Review Game & Answers
RS || WY
If TY = 4, then RS = 4
ST || WX
If RT = 7, then XY = 14
Midsegments
Answers:
Ch 5 Review Game & Answers
Thesamedistancefromtwopoints.
Ch 5 Review Game & Answers
Answer:
Equidistant
Ch 5 Review Game & Answers
B
C
A D
E
F
12y - 8
8y + 20
8x + 6
6x + 18
DE is the perpendicular bisector of AC. Find the indicated measures.
2x + 4y
Find AD.
Find BC.
Is B on the perpendicular bisector of AC?
State the theorem that allows you to set AD ≅ BC?
Ch 5 Review Game & Answers
12x - 8 = 8x + 204x = 28x = 7
Therefore AD = 12(7) - 8 = 76
Answers:
Perpendicular Bisector Theorem
8x + 6 = 6x + 18
Ch 5 Review Game & Answers
8x - 12 2x + 36
Find the value of x.
What theorem allows you to say AB ≅ BC and solve for x?
A
B
C
Ch 5 Review Game & Answers
Answers:
8x - 12 = 2x + 366x = 48x = 8
Angle Bisectors Theorem
Ch 5 Review Game & Answers
12
13
A
B
C
D
EF
G
x-6
Find the value of x.
What is the point of concurrency of theangle bisectors (point G)?
Ch 5 Review Game & Answers
Answers:
Pythagorean theorem states: a2 + b
2 = c
2
122 + b
2 = 13
2
144 + b2 = 169
b2 = 25
b = 5
Therefore, FG = 5 and by the Concurrency of the Angle Bisector Theorem, FG = DG = BG
x-6 = 5x = 11
Incenter
Ch 5 Review Game & Answers
M
N
O
P
QR
S
N, P, and R are the midpoints of ∆MOQ
Find the value of SQ.
What are QN, OR, and MP?
Find the value of x.
QN = 36
164x - 12
Ch 5 Review Game & Answers
Answers:
SQ = QN
SQ = 36
SQ = 24
MS = MP
MS = 32
32 = 4x - 124x = 44x = 11
Medians
Ch 5 Review Game & Answers
Thepointofintersectionofthreeormorelines,rays,orsegments.
Ch 5 Review Game & Answers
Answer:
Point of Concurrency
Ch 5 Review Game & Answers
7 and 24
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.
Ch 5 Review Game & Answers
247
x
247
x
Answers:
Case 1: x is longest side
Case 2: 24 is the longest side
By the Triangle Inequality Theorem
7 + 24 > x31 > x
By the Triangle Inequality Theorem
7 + x > 24x > 17
17 < x < 31
Ch 5 Review Game & Answers
Q
R
S
Find the coordinates of the centroid.
Find the midpoint of SQ (call it T).
Find the length of RT.
Ch 5 Review Game & Answers
Midpoint of SQ:
T =
=
=
Length of RT:
RT = (2-2)2 + (5-(-4))
2
= 02 + 9
2
= 81
= 9
Coordinates of centroid C:
By the Concurrency of the Medians Theorem, RC = RT
RC = 9
RC = 6
Answer:
Ch 5 Review Game & Answers
Thepointofconcurrencyofthethreemediansofatriangle.
Ch 5 Review Game & Answers
Answer:
Centroid
Ch 5 Review Game & Answers
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.
4 and 11
Ch 5 Review Game & Answers
Answer:
Case 1: x is the longest side
4 11
x
4 x
11
4 + 11 > x15 > x
Case 2: 11 is the longest side
4 + x > 11x > 7
7 < x < 15
Ch 5 Review Game & Answers
In ∆LMN, LM = 11, MN = 18, and LN = 24. Sketch and label the triangle.
List the angles in order from smallest to largest.
Ch 5 Review Game & Answers
L
M
N
1118
24
Smallest to largest
∠N, ∠L, ∠M
Answer:
Ch 5 Review Game & Answers
Thepointatwhichthelinescontainingthethreealtitudes ofatriangleintersect.
Ch 5 Review Game & Answers
Answer:
Orthocenter
Ch 5 Review Game & Answers
X
Y
Z
T
U
V
W
Find the value of x.
22
5x-8
What is the point of concurrency of the perpendicular bisectors of a triangle?
Ch 5 Review Game & Answers
Answers:
By the Concurrency of the Perpendicular Bisector Thm, WX = WY = WZ.
Therefore, WY = WZ5x - 8 = 225x = 30x = 6
Circumcenter
Ch 5 Review Game & Answers
WY, 4
WX, 14
Midsegments
Equidistant
76
⊥ Bisector Thm
54
x = 8
∠ Bisector Thm
x = 11
Incenter
24
x = 12
Medians
Point of Concurrency
17 < x < 31
(2,4)
9
(2,1)
Centroid
7 < x < 15
∠N, ∠L, ∠M
Orthocenter
x = 6
Circumcenter
Ch 5 Review Game & Answers
Need to know for the test
Definitions
MidsegmentsPerpendicular BisectorEquidistantConcurrentPoint of ConcurrencyCircumcenterAngle BisectorIncenterMedianCentroidAltitudeOrthocenter
Thoerems (and how to apply them)
Midsegment Thm.Converse of the Midsegment Thm.⊥ Bisector Thm.Converse of ⊥ Bisector ThmConcurrency of ⊥ Bisector of ∆ Thm∠ Bisector ThmConverse ∠ Bisector ThmConcurrency of ∠ Bisector of ∆ ThmConcurrency of Medians of ∆ ThmConcurrency of Altitudes of ∆ ThmTriangle Inequality Theorem
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