Download Lesson 6: Parts and Types of Triangles

Lesson 6
RCSD Geometry Local MATHEMATICS CURRICULUM
U7
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 6: Parts and Types of Triangles
Learning Target:


I can find the unknown angles and cite geometric justifications regarding angles in a triangle
I can identify different types of triangles based on angles and sides
Parts of a Triangle
Each triangle has three __________ and three _______________. Each _______________ is where two sides
meet. A pair of sides and the vertex define an ____________, so each triangle includes three _____________.
Write "side" next to each side and circle the vertices on the
triangle below.
Each vertex is named with a ___________ letter. The sides can
then be named with the letters of the two _____________ on either side of it.
The triangle is named with a triangle symbol Δ in front followed by the three letters of its vertices.
Label the vertices of the triangle at right with 𝑨, 𝑩, and 𝑪
Name the 3 sides of this triangle
______
______
______
Example 1. What is the name of the side shown in red?
Lesson 6
RCSD Geometry Local MATHEMATICS CURRICULUM
U7
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Example 2. What is the name of the side shown in red?
Example 3 Which of the following are names of this triangle?
Types of Triangles
Isosceles: The ____________ angles of an Isosceles triangle (and sides
opposite them) are _________________.
Equilateral: Each angle/side of an equilateral triangle have __________
measures. Each interior angle of an equilateral triangle would have a
measure of _________ degrees. Equilateral triangles are also called
Equiangular ( when all angles are said to be equal)
Scalene: The three angles/sides of a scalene triangle have
_________________ measures.
Right Triangle: A triangle that has one right angle
Draw a picture
Lesson 6
RCSD Geometry Local MATHEMATICS CURRICULUM
U7
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Example 4. An isosceles triangle is _______________ an equilateral triangle.
A. Sometimes
B. Always
C. Never
Example 5. Write true or false for the following statements
 A triangle can have more than one right angle.
 An equilateral triangle is also an isosceles triangle
Example 6. This triangle is classified as _______________________ .
(Choose all that apply.)
Triangle Sum Theorem
In the past we have talked about how the interior angles of a triangle have a sum of 180°…..BUT WHY?
In the diagram below, 𝑙 ∥ 𝑚.
l
m
What is the value of∠ a? ______ Reason: __________________________________________________
What is the value of ∠ b? ______ Reason: __________________________________________________
What is the value of ∠ c? ______ Reason: __________________________________________________
Triangle Sum Theorem:
𝑚∠ 𝒂 + 𝑚∠ 𝑏 + 𝑚∠ 𝑐 = __________
The sum of the 3 angle measures of any triangle is ________.
Lesson 6
RCSD Geometry Local MATHEMATICS CURRICULUM
U7
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Example 1. Find the measure of the missing angle.
Example 2. What is the measurement of the missing angle?
Example 3. In 𝛥𝐴𝐵𝐶, if 𝑚∠𝐵 is 84° and 𝑚∠𝐶 is 36°, what is 𝑚∠𝐴? _________________
Example 4. Solve for w, v and t
Give a reason for each answer:
𝒎∠𝒘 = _________
𝒎∠𝒗 = _________
𝒎∠𝒕 = _________
Example 5. Solve for 3, 4 and 5
Give a reason for each answer:
𝒎∠𝟑 = _________
𝒎∠𝟒 = _________
𝒎∠𝟓 = __________
Example 6. Solve for x
Find the measure of ∠𝑄𝑅𝑃 𝑎𝑛𝑑 ∠𝑃𝑄𝑅
RCSD Geometry Local MATHEMATICS CURRICULUM
Lesson 6
U7
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 6: Parts and Types of Triangles
Problem Set
Directions: For #1-5, solve for the variable (s). Give a reason that justifies your response for each variable.
Remember, you may need to solve for other unknown angles, before you can solve for the specific variable
that is asked.
For Activities 1, 2 and 3, solve for all unknown angles . Give a reason for each answer.
1.
2.
3.
RCSD Geometry Local MATHEMATICS CURRICULUM
Lesson 6
U7
GEOMETRY
Name:___________________________________
Period:________ Date:__________
4. Solve for x.
5. What is the measure of ∠B?
6. Solve for x and y in the diagrams. Explain why the equations you use to solve for x are appropriate and
explain why they equations you used to solve for y are appropriate.
Find the value of 𝑑 and 𝑘:
𝒅 = ________
𝒙 = ________
Lesson 6
RCSD Geometry Local MATHEMATICS CURRICULUM
U7
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 6: Parts and Types of Triangles
Homework
For activities 1 and 2 find the missing angle. Explain your reasoning
1.
2.
3. In the diagram of ∆𝐽𝐸𝐴 at right, 𝑚∠𝐽𝐸𝐴 = 90 and 𝑚∠𝐸𝐴𝐽 = 48.
Line segment MS connects points M and S on the triangle, such that
𝑚∠𝐸𝑀𝑆 = 59. What is ∠𝐽𝑆𝑀 ?
4.
The diagram at right shows ∆𝐴𝐵𝐷, with ⃗⃗⃗⃗⃗⃗⃗⃗
𝐴𝐵𝐶 , ̅̅̅̅
𝐵𝐸 ⊥ ̅̅̅̅
𝐴𝐷, and
∠𝐸𝐵𝐷 ≅ ∠𝐶𝐵𝐷. If 𝑚∠𝐴𝐵𝐸 = 52, what is 𝑚∠𝐷 ?