Transcript Classifying Triangles and Angle Relationships

Welcome to Triangles!
• Pick up new assignment log and notes
• Take out your Animal Project
• Transformation Test will not be given back until Friday at the
earliest
Tonight's homework:
1) Pg. 219 #1-11
2) P 227 # 4-11, 24
3) Classifying Triangles Worksheet ( on back of 4.1 notes)
4) Make notecards on the vocabulary from today’s lesson
Welcome to Triangles!
• Transformations was Unit 2 Part 1
• We are still on Unit 2, but we are now focusing on
TRIANGLES!
On your whiteboard, write down everything you know
about triangles.
Do Now!:Whiteboards
Classify each angle as acute, obtuse, or right.
1.
2.
3.
4. What are the possible degrees of an acute, obtuse,
right, and straight angle.
Agenda




U2L5- Classifying Triangles
U2L6- Angles Relationships in Triangles
Proving the Triangle Sum Theorem
Cool-Down…
You will get your Transformation Test at the earliest on Friday
4.1: Classifying Triangles
Learning Objective
SWBAT classify triangles by their angle measures and
side lengths.
How to Classify Triangles
Todays topic is all about classifying triangles, meaning
what category do they fall under.
We can classify triangles two ways:
1. By their angle measures.
2. By their side lengths.
How to Classify Triangles:
NOTE:
By Angle Measures
When you look at a figure, you cannot assume
segments or angles are congruent based on
appearance. They must be marked as congruent using
tick or arc marks.
4-1 Classifying Triangles
Lets recall how to label the sides and angles.
C
A
B
AB, BC, and AC are the sides of
A, B, C are the triangle's vertices.
ABC.
4-1 Classifying Triangles
Triangle Classification By Angle Measures
Acute Triangle
Three acute angles
4-1 Classifying Triangles
Triangle Classification By Angle Measures
Equiangular Triangle
Three congruent acute angles
4-1 Classifying Triangles
Triangle Classification By Angle Measures
Right Triangle
One right angle
4-1 Classifying Triangles
Triangle Classification By Angle Measures
Obtuse Triangle
One obtuse angle
Classifying by Side Lengths
Triangle Classification By Side Lengths
Equilateral Triangle
Three congruent sides
4-1 Classifying Triangles
Triangle Classification By Side Lengths
Isosceles Triangle
At least two congruent sides
4-1 Classifying Triangles
Triangle Classification By Side Lengths
Scalene Triangle
No congruent sides
Example 1
By Angle Measures
Whiteboards
Classify
ABD by its angle measures.
Whiteboards
1. Classify ACD by its side lengths.
2. Classify ADB by its side lengths.
3. Classify ACB by its side lengths.
4-1 Classifying Triangles
Example 2
Find the side lengths of
By Angle Measures
JKL.
Whiteboards
Find the side lengths of equilateral
FGH.
Whiteboards
Classify each triangle by its angles and sides.
1. MNQ
2. NQP
3. MNP
Closure for 4.1
On your whiteboard, draw and label your triangle.
By Angle Measures
Classify your triangle by the Angles and the Side
Lengths!
Find someone in the room ( that is NOT at your table)
with the same classification as you!
MATH JOKE OF THE DAY
• How many feet are in a yard?
• It depends on how many people are in the
yard!
4.2: Angle Relationships in Triangles
• Learning Objective
– SWBAT find the measures and apply theorems of
interior and exterior angles of triangles.
Developing the Triangle Sum Theorem
Materials
Scratch piece of paper
Straightedge
Scissors
Directions
1. Using a straightedge, draw a triangle and
label the angles A,B,C INSIDE the triangles (
look at whiteboard)
2. Cut the triangle out and the angles.
3. Try to form a straight line with the angles.
Reflection
Answer the three questions on your notes
1) What do you notice about the three angles of the
triangle?
1) Look at your table-mates triangles. Did they notice
the same thing or different?
1) Write an equation describing the relationship among
the measures of the interior angles in a triangle.
Congrats!
You just figured out the Triangle Sum Theorem

Recall
Remember back to Unit 1, when we added a line
to help us solve the following type of problem
Well, that is called an auxiliary line.
An auxiliary line is a line that is added to a figure to aid in a
proof.
4
C
Y
2
1
X
5
An auxiliary line used in the
Triangle Sum Theorem
2
A
3
B
Brainstorm for Triangle Sum Theorem
On your whiteboards, answer the following questions:
C
4
2
A
X
1
5
3
B
What is the relationship between angles 1 and 4?
What is the relationship between angles 3 and 5?
Using the angle addition postulate, what do angles 1, 2 and 3 equal?
Proof of Triangle Sum Theorem
Proof of Triangle Sum Theorem
With your table, put the following cards in order.
When you are done, raise your hand and I will
check it off and then you will write it on your
guided notes.
Use each card once.
Example 1
Whiteboards
After an accident, the positions of cars are
measured by law enforcement to
investigate the collision. Use the diagram
drawn from the information collected to
find the following:
1. mXYZ.
2. mYWZ
Table-Share
What is the measure of each angle of an
equiangular triangle?
Write your thoughts on your whiteboard.
Table-Share
What is the relationship between the two other
angles in a right triangle?
Write your thoughts on your whiteboard.
Congrats!
You just formed the two corollaries by yourself!
A corollary is a theorem whose proof follows directly from
another theorem. Here are two corollaries to the Triangle Sum
Theorem.
Example 2: Finding Angle Measures in
Right Triangles
One of the acute angles in a right triangle
measures 2x°. What is the measure of the other
acute angle?
Let the acute angles be A and B, with mA = 2x°.
mA + mB = 90°
2x + mB = 90
mB = (90 – 2x)°
Whiteboards
• The measure of one of the acute angles in a
right triangle is x°. What is the measure of
the other acute angle?
Interior
• all points inside the figure
Exterior
• all points outside the figure.
1.
What are the interior angles?
2.
What are the exterior angles?
Exterior
Interior
Exterior Angle Theorem
The measure of an exterior angle of a
triangle is equal to the sum of the
measures of its non-adjacent interior
angles
4= 1 + 2
Example 3: Applying the Exterior Angle
Theorem
Find mB.
Whiteboards
Find mACD.
Third Angle Theorem
Example 4: Applying the Third Angle
Theorem
Find mK and mJ.
Whiteboards
Find mP and mT.