Aim #3: What is the Side Splitter Theorem?
CC Geometry H
Do Now: a. In the diagram shown, identify the scale factor (r) applied if OB = 5
and OB' = 9.
B'
B
b. If OA = 7, find the measure of OA'.
O
A'
A
Side Splitter Theorem
We've used the ratio method to create scale drawings.
In the diagram below, we notice after a dilation with scale factor r and center O,
AB || A'B'.
OB' if and only if AB || A'B'
The Side Splitter Theorem states: OA'
=
OB
OA
a. With a ruler and in mm, measure the segments in the figure below to verify that
B'
the following proportion is true: OA' OB'
=
OB
d
OA
B
c
b. Is the proportion
OA OB
also true?
=
OA' OB'
c. Is the proportion
AA' BB'
also true?
=
OA' OB'
d. Is the proportion
OA AA'
also true?
=
OB BB'
O
a
A
b
A'
1) In ∆ABC, AB
BC and DE
BC. If AD = 9, DC = 15 and EC = 10,
a) Find BC.
A
D
b) Find AB to the nearest tenth.
B
E
C
2) BC = x, EC = x - 7, AD = 21, DC = 24. Find BE.
A
>
B
E
>
D
C
3) In ΔACT, BE || AT. If CB = 3, CA = 10, and CE = 6, what is the length of ET?
4) Can the following conclusions be drawn from the diagram shown?
a) The side splitter VW is parallel to the third side
of the triangle by the Triangle Side Splitter Theorem.
V
1.5
U
2
6
X
W
b) ≮Y ≅ ≮UWV because corresponding angles
formed by parallel lines cut by a transversal are congruent.
4.5
Y
4
c) UX = 7 UV
d) ΔUXY is a scale drawing of ΔUVW with a scale factor of
7
4.
5) Find x and y. The diagram is not drawn to scale.
Let's Sum it Up!
If a segment intersects two sides of a triangle and is parallel to the third side,
the ratio of the lengths of the segments on one side of the triangle equals the
ratio of the lengths of the corresponding segments of the other side.
Name ______________________
Date ________________
CC Geometry H
HW #3
B
In the diagram, XY || AC. Use the diagram to answer #s 1-2.
1. If BX = 4, BA = 5, and BY = 6, find the measure of BC.
Y
X
C
A
Not drawn to scale
2. If BX = 9, BA = 15, and BY = 15, find the measure of YC.
3. In ΔADE, B is a point on AE and C is a point on AD such that BC || ED. If
AC = x - 3, BE = 20, AB = 16, and AD = 2x + 2, find the length of AC.
o
o
4. Given the diagram, AC = 12, AB = 6, BE = 4, ≮ACB = x , and ≮D = x , find CD.
5. Solve for x:
a.
b.
6. Find the scale factor used in the scale drawing below which applied the ratio
method if OA'= 45 units and OA = 22.5:
O
Review:
1) Find x and AB if AB is a midsegment of triangle ABC:
2) ΔABC has coordinates A(-13,3), B(3,-1), and C(4,4). Graph and label ΔA"B"C",
the image of ΔABC after the translation 2 units to the right and five units up
followed by a reflection over the line y = 0.