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

Y

W

X

U

ZV

8.7

15.2

7.4

5c

3b + 2 2a

Points U, V, and W are midpoints of YZ, ZX, and XY. Find a, b, and c.

Practice Problems

BA

C

DE

5.2

6.1

4.8

5.3 5.4

5.6

6.4

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

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

NL

D

141 9a + 15

12 12

1618

Practice Problems

11

8

8

9

7n + 5

47

X

W

Y

Z

Compare angle WYX and angle ZYW. Write an inequality statement and solve for n.

Practice Problems

L

Q

M

O

NP

A

In the figure, A is the circumcenter of triangle LMN. Find y if LO=8y + 9, ON=12y – 11 and NP= 10y + 4

Practice Problems

L

Q

M

O

NP

A

In the figure, A is the circumcenter of triangle LMN. Find x if the measure of angle APM= 7x + 13

Practice Problems

R

SU

V

T

In triangle RST, RU is an altitude and SV is a median. Find RV if RV=6a + 3 and RT= 10a + 14

Practice Problems

R

ST

62

6355

Refer to the triangle below, Determine the relationship between lengths of RS and ST.

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 2(8.7)=3b+2 2(5c)=15.2

4a=7.4 17.4=3b+2 10c=15.2

a=1.85 b=5.13333 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