use wxy, where r, s, and t are midpoints of the sides....
TRANSCRIPT
![Page 1: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/1.jpg)
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?
![Page 2: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/2.jpg)
Ch 5 Review Game & Answers
RS || WY
If TY = 4, then RS = 4
ST || WX
If RT = 7, then XY = 14
Midsegments
Answers:
![Page 3: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/3.jpg)
Ch 5 Review Game & Answers
Thesamedistancefromtwopoints.
![Page 4: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/4.jpg)
Ch 5 Review Game & Answers
Answer:
Equidistant
![Page 5: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/5.jpg)
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?
![Page 6: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/6.jpg)
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
![Page 7: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/7.jpg)
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
![Page 8: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/8.jpg)
Ch 5 Review Game & Answers
Answers:
8x - 12 = 2x + 366x = 48x = 8
Angle Bisectors Theorem
![Page 9: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/9.jpg)
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)?
![Page 10: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/10.jpg)
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
![Page 11: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/11.jpg)
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
![Page 12: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/12.jpg)
Ch 5 Review Game & Answers
Answers:
SQ = QN
SQ = 36
SQ = 24
MS = MP
MS = 32
32 = 4x - 124x = 44x = 11
Medians
![Page 13: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/13.jpg)
Ch 5 Review Game & Answers
Thepointofintersectionofthreeormorelines,rays,orsegments.
![Page 14: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/14.jpg)
Ch 5 Review Game & Answers
Answer:
Point of Concurrency
![Page 15: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/15.jpg)
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.
![Page 16: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/16.jpg)
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
![Page 17: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/17.jpg)
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.
![Page 18: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/18.jpg)
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:
![Page 19: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/19.jpg)
Ch 5 Review Game & Answers
Thepointofconcurrencyofthethreemediansofatriangle.
![Page 20: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/20.jpg)
Ch 5 Review Game & Answers
Answer:
Centroid
![Page 21: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/21.jpg)
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
![Page 22: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/22.jpg)
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
![Page 23: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/23.jpg)
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.
![Page 24: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/24.jpg)
Ch 5 Review Game & Answers
L
M
N
1118
24
Smallest to largest
∠N, ∠L, ∠M
Answer:
![Page 25: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/25.jpg)
Ch 5 Review Game & Answers
Thepointatwhichthelinescontainingthethreealtitudes ofatriangleintersect.
![Page 26: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/26.jpg)
Ch 5 Review Game & Answers
Answer:
Orthocenter
![Page 27: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/27.jpg)
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?
![Page 28: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/28.jpg)
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
![Page 29: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/29.jpg)
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
![Page 30: Use WXY, where R, S, and T are midpoints of the sides. …kentschools.net/ehughes/files/2011/12/Ch-5-Review-Game-Answers.pdf... where R, S, and T are midpoints of the sides. X Y W](https://reader035.vdocuments.us/reader035/viewer/2022081505/5aff3fb57f8b9a256b8e37d1/html5/thumbnails/30.jpg)
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