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!:WhiteboardsClassify 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.

By Angle Measures

How to Classify Triangles:

NOTE: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 TrianglesLets recall how to label the sides and angles.

B

AC

AB, BC, and AC are the sides of ABC.

A, B, C are the triangle's vertices.

Acute Triangle

Three acute angles

Triangle Classification By Angle Measures

4-1 Classifying Triangles

Equiangular Triangle

Three congruent acute angles

Triangle Classification By Angle Measures

4-1 Classifying Triangles

Right Triangle

One right angle

Triangle Classification By Angle Measures

4-1 Classifying Triangles

Obtuse Triangle

One obtuse angle

Triangle Classification By Angle Measures

4-1 Classifying Triangles

Equilateral Triangle

Three congruent sides

Triangle Classification By Side Lengths

Classifying by Side Lengths

Isosceles Triangle

At least two congruent sides

Triangle Classification By Side Lengths

4-1 Classifying Triangles

Scalene Triangle

No congruent sides

Triangle Classification By Side Lengths

4-1 Classifying Triangles

By Angle Measures

Example 1

Classify ABD by its angle measures.

Whiteboards

Whiteboards

1. Classify ACD by its side lengths.2. Classify ADB by its side lengths.3. Classify ACB by its side lengths.

By Angle Measures

4-1 Classifying Triangles

Example 2Find the side lengths of JKL.

Find the side lengths of equilateral FGH.

Whiteboards

Whiteboards

Classify each triangle by its angles and sides.1. MNQ 2. NQP 3. MNP

By Angle Measures

Closure for 4.1 On your whiteboard, draw and label your triangle.

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

MaterialsScratch piece of paperStraightedge Scissors

Directions1. 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.

ReflectionAnswer the three questions on your notes

1) What do you notice about the three angles of the triangle?

2) Look at your table-mates triangles. Did they notice the same thing or different?

3) 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.

An auxiliary line used in the Triangle Sum Theorem

1 54 

2 3

A B

CY2

X

Brainstorm for Triangle Sum TheoremOn your whiteboards, answer the following questions:

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?

1 54 

2 3A B

C X

Proof of Triangle Sum Theorem

Proof of Triangle Sum TheoremWith 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

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. mXYZ.2. mYWZ

Whiteboards

Table-ShareWhat is the measure of each angle of an equiangular triangle?

Write your thoughts on your whiteboard.

Table-ShareWhat 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.

One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle?

mA + mB = 90°

2x + mB = 90

mB = (90 – 2x)°

Let the acute angles be A and B, with mA = 2x°.

Example 2: Finding Angle Measures in Right Triangles

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.

Interior

Exterior1. What are the interior angles?

2. What are the exterior angles?

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 mB.

Whiteboards

Find mACD.

Third Angle Theorem

Example 4: Applying the Third Angle Theorem

Find mK and mJ.

Whiteboards

Find mP and mT.