Ch 5 Review Game & Answers
Use ∆WXY, where R, S, and T are midpoints of the sides.
T
W
Y
RS || _____
If TY = 4, then RS = _____
R
S
ST || _____
If RT = 7, then XY = _____
What are TR, RS, and ST called?
X
Ch 5 Review Game & Answers
Answers:
RS || WY
If TY = 4, then RS = 4
ST || WX
If RT = 7, then XY = 14
Midsegments
Ch 5 Review Game & Answers
The
same
distance
from
two
points.
Ch 5 Review Game & Answers
Answer:
Equidistant
Ch 5 Review Game & Answers
6x + 18
C
B
F
E
8y + 20
8x + 6
2x + 4y
A
12y - 8
D
Find AD.
State the theorem that allows you to set AD ≅ BC?
Find BC.
Is B on the perpendicular bisector of AC?
DE is the perpendicular bisector of AC. Find the indicated
measures.
Ch 5 Review Game & Answers
Answers:
12x - 8 = 8x + 20
4x = 28
x=7
Therefore AD = 12(7) - 8 = 76
Perpendicular Bisector Theorem
8x + 6 = 6x + 18
Ch 5 Review Game & Answers
B
8x - 12
A
2x + 36
C
Find the value of x.
What theorem allows you to say AB ≅ BC and solve for x?
Ch 5 Review Game & Answers
Answers:
8x - 12 = 2x + 36
6x = 48
x=8
Angle Bisectors Theorem
Ch 5 Review Game & Answers
A
12
13
F
E
G
x-6
D
B
C
Find the value of x.
What is the point of concurrency of the
angle bisectors (point G)?
Ch 5 Review Game & Answers
Answers:
2
2
Pythagorean
theorem
states: a + b = c
2
2
2
12 + b 2 = 13
144
+ b = 169
2
b = 25
b=5
2
Therefore, FG = 5 and by the Concurrency of the Angle Bisector
Theorem, FG = DG = BG
x-6 = 5
x = 11
Incenter
Ch 5 Review Game & Answers
N, P, and R are the midpoints of ∆MOQ
O
QN = 36
N
S
4x - 12
16
P
M
R
Q
Find the value of SQ.
Find the value of x.
What are QN, OR, and MP?
Ch 5 Review Game & Answers
Answers:
SQ =
QN
SQ =
36
SQ = 24
MS =
MP
MS = 32
32 = 4x - 12
4x = 44
x = 11
Medians
Ch 5 Review Game & Answers
The
point
of
intersection
of
three
or
more
lines,
rays,
or
segments.
Ch 5 Review Game & Answers
Answer:
Point of Concurrency
Ch 5 Review Game & Answers
Describe the possible lengths of the third side of the
triangle given the lengths of the other two sides.
7 and 24
Ch 5 Review Game & Answers
Answers:
Case 1: x is longest side
By the Triangle Inequality Theorem
24
7
7 + 24 > x
31 > x
x
Case 2: 24 is the longest side
By the Triangle Inequality Theorem
24
7
x
17 < x < 31
7 + x > 24
x > 17
Ch 5 Review Game & Answers
Find the midpoint of SQ (call it T).
Q
Find the length of RT.
S
R
Find the coordinates of the centroid.
Ch 5 Review Game & Answers
Answer:
Midpoint of SQ:
T=
=
=
Length of RT:
RT =
2
(2-2) + (5-(-4))
2
= 0 +9
2
2
= 81
= 9
Coordinates of centroid C:
By the Concurrency of the Medians Theorem, RC =
RC =
RC = 6
9
RT
Ch 5 Review Game & Answers
The
point
of
concurrency
of
the
three
medians
of
a
triangle.
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
11
4
4 + 11 > x
15 > x
x
Case 2: 11 is the longest side
x
4
11
7 < x < 15
4 + x > 11
x>7
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
Answer:
M
11
18
L
24
Smallest to largest
∠N, ∠L, ∠M
N
Ch 5 Review Game & Answers
The
point
at
which
the
lines
containing
the
three
altitudes of
a
triangle
intersect.
Ch 5 Review Game & Answers
Answer:
Orthocenter
Ch 5 Review Game & Answers
Find the value of x.
Y
T
22
U
W
X
5x-8
V
Z
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 = WZ
5x - 8 = 22
5x = 30
x=6
Circumcenter
Ch 5 Review Game & Answers
WY, 4
x = 11
(2,1)
WX, 14
Incenter
Centroid
Midsegments
24
7 < x < 15
Equidistant
x = 12
∠N, ∠L, ∠M
76
Medians
⊥ Bisector Thm
Point of Concurrency
54
17 < x < 31
x=8
(2,4)
∠ Bisector Thm
9
Orthocenter
x=6
Circumcenter
Ch 5 Review Game & Answers
Need to know for the test
Definitions
Thoerems (and how to apply them)
Midsegments
Perpendicular Bisector
Equidistant
Concurrent
Point of Concurrency
Circumcenter
Angle Bisector
Incenter
Median
Centroid
Altitude
Orthocenter
Midsegment Thm.
Converse of the Midsegment Thm.
⊥ Bisector Thm.
Converse of ⊥ Bisector Thm
Concurrency of ⊥ Bisector of ∆ Thm
∠ Bisector Thm
Converse ∠ Bisector Thm
Concurrency of ∠ Bisector of ∆ Thm
Concurrency of Medians of ∆ Thm
Concurrency of Altitudes of ∆ Thm
Triangle Inequality Theorem