8.4 Proportionality Theorems with answers8.4 Proportionality
Theorems
Refer to Section 84 (pg 446) for
additional help/practice
8.4 Proportionality Theorems with answers
Triangle Proportionality Theorem
•
If a line is parallel to a side of a triangle and
intersects the other two sides, then it divides
those sides proportionally.
A
8.4 Proportionality Theorems with answers
Current Old Cable Bridge
150 ft 250 ft
Application: Justin uses triangles to find the distance across the
Trinity river. He makes the diagram below. Which triangles appear to
be similar? What must Justin know about these triangles to conclude
that they are similar? What is the distance of the new bridge?
8.4 Proportionality Theorems with answers
A
B D C
Triangle Angle Bisector Theorem •
An angle bisector of a triangle divides the
opposite side into two segments whose lengths
are proportional to the lengths of the other two
sides.
Then:
IF:
X = 3
Practice: Solve for x if SV is an angle bisector.
8.4 Proportionality Theorems with answers
Practice: If AC is twice as long as AB, what is the
length of DC?
A
B D Cx2.5 cmF. 2.5 cm
G. 3.75 cm
H. 5 cm Correct
J. 15 cm
Hint: Move answers to triangle to check answer
8.4 Proportionality Theorems with answers
Two-Transversal Proportionality:
•
If 3 or more parallel lines intersect two
transversals, they cut off the transversals
proportionally.
If: A
Hint: drag the ratio to the box to find proportion.
8.4 Proportionality Theorems with answers
Application: Suppose that an artist decided to make a
larger sketch of the trees. 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.
8.4 Proportionality Theorems with answers
4
x
8.4 Proportionality Theorems with answers
HW: pg. 450: 3, 5, 13, 15, 17, 21, 23, 25, 41 45
8.4 Proportionality Theorems with answers
DAY TWO Warm up:
8.4 Proportionality Theorems with answers
y = 18 CD = 15
E
In the diagram below, a metal support brace is added to stabilize a
metal triangle. The metal brace is parallel to the base and divides
the left side into a 4.5-foot and 8-foot section. Find the length
of CD.
Check the answer by moving the triangle.
8.4 Proportionality Theorems with answers
Application
1. The perimeter of triangle ABC is 29 m. AD bisects angle A.
Find AB and AC. B
A C
4 m
5 m D
2. Given that DE II BC, XY ll AD. Find EC.
A X
8.4 Proportionality Theorems with answers
Practice 8.4 WS Test Friday
HW due Thursday includes: • 8.1 pg. 423 •
8.2 pg. 431 • 8.3 pg. 441 •
8.4 pg. 450 • 8.4 WS • Test Review
8.4 Proportionality Theorems with answers
Quizziz Grade
22 Questions
When done pick up your test review and check
your entry ticket from yesterday online.
Tomorrow, CHROMEBOOK Quizlet Live, go
over test review, and homework due!
8.4 Proportionality Theorems with answers
1) Get out Test Review to go over it and ask
questions.
2) Homework due in folder! Including this test
review.
3) Quizlet Live on Chromebook!
4) Test Tomorrow!
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
8.4 Proportionality Theorems with answers
1) Get out Test Review to go over it and ask
questions.
2) Homework due in folder! Including this test
review.
3) Quizlet Live on Chromebook!
4) Test Tomorrow!
SMART Notebook
SMART Notebook
SMART Notebook
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