Download Chapter 5 Review

Chapter 5 Review
Segments in Triangles
Test Outline
• Multiple Choice
– Be able to identify vocab (pick out from a picture)
– Be able to apply SAS and SSS Inequality Theorems
(biggest angle across from biggest side)
– Identify longest/shortest segment and/or
largest/smallest angle, also list all sides or angles
from least to greatest or greatest to least
– Determine if three lengths can be the sides of a
triangle
Test Outline Continued
• Short Answer/Solving Problems
– Be able to use equations that go with
centroids, circumcenters, medians, and
altitudes to solve problems involving algebra
– Be able to list segments and angles from least
to greatest in a given triangle
Test Ouline Continued
• Indirect Proofs
– Be able to write an indirect proof involving two
triangles from start to finish
• Three step process
– 1. assume that ….
– 2. then…. This contradicts…
– 3. Therefore…
Test Outline Continued
• Write and solve inqualities between two
triangles
– Be able to use the SAS and SSS Inequalities
to write and solve inequalities relating the
sides or angles of triangles
Practice Problems
Points U, V, and W are midpoints of YZ, ZX, and XY. Find a, b, and c.
Y
7.4
W
U
8.7
5c
3b + 2
15.2
2a
Z
X
V
Practice Problems

A.Determine the relationship between the measures of angle ABD and
angle DAB
B. List the angles of triangle BCD in order from least to greatest
A
B
5.6
4.8
5.4
5.3
6.4
C
6.1
E
5.2
D
Practice Problems
Determine whether the measures 6.8, 7.2,
and 5.1 can be lengths of the sides of a
triangle.
Practice Problems
• Write and inequality relating angle LDM to
MDN using the information in the figure.
Find a.
M
18
16
141
9a + 15
D
12
L
12
N
Practice Problems
Compare angle WYX and angle ZYW. Write an inequality statement
and solve for n.
W
11
X
9
8
7n + 5
Z
47
8
Y
Practice Problems
In the figure, A is the circumcenter of triangle LMN. Find y if LO=8y + 9,
ON=12y – 11 and NP= 10y + 4
L
O
Q
A
M
N
P
Practice Problems
In the figure, A is the circumcenter of triangle LMN. Find x if the
measure of angle APM= 7x + 13
L
O
Q
A
M
N
P
Practice Problems
In triangle RST, RU is an altitude and SV is a median. Find RV if
RV=6a + 3 and RT= 10a + 14
R
V
T
U
S
Practice Problems
Refer to the triangle below, Determine the relationship between lengths
of RS and ST.
R
62
55
T
63
S
Practice Problems
Write the assumption you would make to
start an indirect proof of the statement:
Triangle ABC is congruent to triangle DEF
Practice Problems
Can the measures of 5, 7, and 8 be the
lengths of the sides of a triangle?
Practice Problems
Find the range for the measure of the third
side of a triangle if two of its sides
measure 4 and 13.
Practice Problem answers:
2(2a)=7.4
4a=7.4
a=1.85
2(8.7)=3b+2
17.4=3b+2
b=5.13333
2(5c)=15.2
10c=15.2
c=1.52
Practice Problem answers:
a. Angle ABD > angle DAB
b. Angle D < angle C < angle B
Practice Problem answers:
5.1 + 6.8 = 11.9
11.9>7.2
Yes, because the sum of the two smallest
sides is greater than the third side.
Practice Problem answers:
Angle LDM > Angle MDN
141>9a+15
a<14
Practice Problem answers:
Angle WYX > Angle ZYW
7n+15>47
n>6
Practice Problem answers:
Perpendicular bisectors split the opposite
side into 2 congruent segments
8y+9=12y-11
y=5
Practice Problem answers:
Perpendicular bisectors make right angles
with the opposite side
7x+13=90
x=11
Practice Problem answers:
Medians go to the midpoint which splits the
opposite side into 2 congruent segments
2(6a+3)=10a+14
12a +6=10a+14
a=4
Practice Problem answers:
Assume that triangle ABC is not congruent
to triangle DEF.
Practice Problem answers:
5+7=12
12>8
Yes, because the sum of the two smallest
sides is greater than the third side.
Practice Problem answers:
13-4<x<13+4
9<x<17