Download Lesson 2: Triangle Side

Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:__________________________________
M2
Period: ________ Date: __________
Lesson 2: Triangle Side- Splitter
Learning Target: I can use the side splitter theorem, which states that a segment splits two sides of a
triangle proportionally if and only if it is parallel to the third side to find the missing sides.
Previously we learned ….
There are two properties of scale drawing/dilations of a figure:
1. Corresponding angles are ________________ in measurement
2. Corresponding lengths and sides are _____________________ in measurement.
Opening Exercise
Using the ratio method to dilate triangle ABC by the rule 𝑫𝑨,𝟑 .
Using a box as 1 unit find each of the following
measurements
AC = ______ AB = ______ BC= ________
AC’ = ______ AB’= ______ B’C’= _______
Fill in the following proportional statement
𝐴𝐶′
=
𝐴𝐵′
=
𝐵𝐶
=
Consider the following measurements find the measures of the other two angles
𝑚∠𝐵 = 60
𝑚∠𝐵′ = ______
𝑚∠𝐶 = 30
𝑚∠𝐶′ = ______
If ______________________________ angles are congruent then segment BC ____ B’C’.
What can we say about the following ratios?
𝐴𝐶
= __________
𝐶𝐶′
𝐴𝐵
𝐵𝐵′
= _______
Conclusion: When a segment is created in a triangle such that the segment is parallel to the third side,
then it divides the other sides proportionally. This segment is called side splitter.
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:__________________________________
M2
Period: ________ Date: __________
Triangle side splitter theorem: A line segment splits two sides of a triangle proportionally
if and only if it is parallel to the third side.
Restatement of the triangle side splitter theorem:
In ∆OA′B′,
̅̅̅̅ splits the sides proportionally
AB
=
or
=
if and only if ___________|| ___________
Use the side-splitter theorem to solve for x in the triangles below.
1.
Show your work
2.
Try on your own ( 4 mins)
3. Given the diagram, 𝐴𝐶 = 12, 𝐴𝐵 = 6, 𝐵𝐸 = 4, 𝑚∠𝐴𝐶𝐵 = 28°, and 𝑚∠𝐷 = 28°
What is the relationship between segment CB and DE? Explain why?
What can you say about the following ratios? Explain your reasoning
𝐴𝐶
𝐴𝐷
𝐴𝐵
𝐴𝐸
𝐶𝐵
𝐷𝐸
Find the length of AD ___________
Find the length of CD ___________
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:__________________________________
M2
Period: ________ Date: __________
Lesson 2: Triangle Side- Splitter
Problem Set
̅̅̅̅̅ a side-splitter? Justify your answer with algebraic work and a written
1. Is line segment 𝑉𝑊
explanation.
̅̅̅̅ . Use the diagram to answer the following Problems 2 & 3:
̅̅̅̅ ∥ 𝐴𝐶
In the diagram at right, 𝑋𝑌
2. If 𝐵𝑋 = 4, 𝐵𝐴 = 5, and 𝐵𝑌 = 6, what is 𝐵𝐶?
3. If 𝐵𝑋 = 9, 𝐵𝐴 = 15, and 𝐵𝑌 = 15, what is 𝑌𝐶?
Not drawn to scale
Use the side-splitter theorem to solve for x in each of the diagrams below.
4.
5.
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:__________________________________
Lesson 2
M2
Period: ________ Date: __________
̅̅̅̅ , 𝐴𝐷 = 3, 𝐷𝐵 = 2, 𝑎𝑛𝑑 𝐷𝐸 = 6 . Find the length of
6. In the diagram of ∆𝐴𝐵𝐶 below, ̅̅̅̅
𝐷𝐸 ∥ 𝐵𝐶
̅̅̅̅
𝐵𝐶 .
̅̅̅̅ ∥ ̅̅̅̅
7. In the diagram below of ∆𝐴𝐷𝐸, B is a point on ̅̅̅̅
𝐴𝐸 and C is a point on ̅̅̅̅
𝐴𝐷 such that 𝐵𝐶
𝐸𝐷 ,
̅̅̅̅ .
𝐴𝐶 = 𝑥 − 3, 𝐵𝐸 = 20, 𝐴𝐵 = 16, and 𝐴𝐷 = 2𝑥 + 2 . Find the length of 𝐴𝐶
8. In ∆𝐴𝐵𝐶 , ̅̅̅̅
𝐷𝐸 is drawn parallel to ̅̅̅̅
𝐴𝐶 . Using the a ruler, determine the lengths AD, DB, CE, EB,
DE, and AC in millimeters. Use these lengths to form ratios and to determine if there is a
relationship between any of the ratios. What can you say about segment ̅̅̅̅
𝐷𝐸 ?
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:__________________________________
M2
Period: ________ Date: __________
Lesson 2: Triangle Side- Splitter
Homework
Use the side-splitter theorem to solve for x in each of the diagrams below.
1.
2.
3.
4.
5.
6.
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:__________________________________
Lesson 2
M2
Period: ________ Date: __________