Geometry – Unit 5 Practice
Side-Splitting
Name: _____________________________!
G.CO.C.10
Date: ___________ Pd: ____
PROOF:
Given: EF BC
AE AF

Prove:
EB FC
Complete the following proof:
Part 1: Show that AEF ABC .
Since EF BC , you can conclude that 1  2 and 3  4 by
__________________________________________________________________________________
So, AEF ABC by _______________________________________________________________
Part 2: Use the fact that corresponding sides of similar triangles are proportional.
STATEMENT
equals
REASON
Corresponding sides are
proportional.
Segment Addition Postulate
AB
AE
AE  EB
AE
EB
1
AE
EB
AE
ab a b
 
c
c c
Subtraction Property of Equality
REFLECTION: Explain how to conclude AEF ABC without using 3 and 4 _______________________
_________________________________________________________________________________________
Complete:
SNRPDP
Unit 5: Triangles and Triangle Congruence
NVACS – Revised 2015-2016
Page 1 of 7
Practice – Unit 5 (cont.)
PROOF:
AE AF

EB FC
Prove: EF BC
Given:
Complete the following proof:
Part 1: Show that AEF ABC .
AE AF
It is given that
and taking the reciprocal of both sides shows that ____________________.

EB FC
AE
AF
Now add 1 to both sides by adding
to the left side and
to the right side. This results in
AE
AF
_________________________________. Adding and using Segment Addition gives
_________________________________. Since A  A , AEF ABC by ___________________.
Part 2: As corresponding angles of similar triangles, AEF  ___________ . Therefore, EF BC by
________________________________________.
REFLECTION: A student states that UV must be parallel to ST . Do you
agree? Why or why not? _______________________________
____________________________________________________
Complete:
PRACTICE:
1) Find the length of QU .
2) Find the length of KL .
Page 2 of 7
Practice – Unit 5 (cont.)
4) Given AB  31mm , BC  19mm ,
CD  27mm , and DE  23mm . Determine
whether BD AE .
3) Determine whether QT RS .
Additional Side-Splitting Theorems/Applications:
Theorem
If three parallel lines
intersect two
transversals, then they
divide the transversals
proportionally.
Hypothesis
Conclusion
UW VX UY
=
=
WY XZ VZ
PRACTICE:
5) A farmer’s land is divided by a newly constructed interstate. The distances shown are in meters. Find
the distance CA between the north border and the south border of the farmer’s land.
6) Find the length of AB .
Page 3 of 7
Practice – Unit 4 (cont.)
Angle Bisector Theorem:
Theorem
If a ray bisects an angle of
a triangle, then it divides
the side into segments whose
lengths are proportional to
the lengths of the other two
sides.
Hypothesis
Conclusion
AD AC

BD BC
PRACTICE:
7) In the diagram, DEG  GEF . Use the given side lengths to find the length of DG .
8) In the diagram, DEG  GEF . Use the given side lengths to find the length of DG .
9) Find the length of AB .
MIXED PRACTICE:
10) In the figure, DE AB . What is the value of x?
A) 9
B) 16
C) 10
D) 2.5
Page 4 of 7
Practice – Unit 4 (cont.)
11) In the figure, PQ ST . What is the value of x?
A) 10
B) 14
C) 5
D) 8
12) In the figure, AB DE . What is the value of y?
A) 9
B) 15
C) 12
D) 6
13) Find the value of x.
14) Verify that DE BC .
Page 5 of 7
Practice – Unit 4 (cont.)
15) Suppose that the artist decided to make a larger sketch of the trees shown below. In the figure, if AB = 4.5
in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in., find LM and MN to the nearest tenth of an inch.
Given: AK BL CM DN
16) Find SR and PS.
17) Find the value of x.
18) Find the value of x.
Page 6 of 7
Practice – Unit 4 (cont.)
19) Show that MO NO .
20) Given that AC = 12, CD = 6, and BA = 15, find the value of DB.
Page 7 of 7