HONORS GEOMETRY4.1. Classifying Triangles

Do Now: No need to write things- just discuss with someone near you.

•What is a triangle?•How many sides does a triangle have?

•How many angles does a triangle have?

Triangles

• For the next unit we will be talking about TRIANGLES

• And to classify triangles we can talk about either their ANGLES or their SIDES

Realize:

•When classifying triangles by angles…. • Two angles in a triangle are always acute--- therefore, we use the third one to classify the triangles by angles!

Types of Triangles (angles)

•1. Acute Triangle•2. Equiangular Triangle•3. Obtuse Triangle•4. Right Triangle

Acute Triangle

Acute Triangle

•Has 3 acute angles

Equiangular Triangle

Equiangular Triangle

•Has three congruent angles!

• Pause…. What are the angles equal to???

• Which means what other type of triangle do we have?

Obtuse Triangle

Obtuse Triangle

•One Obtuse Angle

Right Triangle

Right Triangle

•One Right Angle

Example One:

Example Two:

Classify the following triangles as acute, equiangular, obtuse, or right. Explain your reasoning.△PQR QSR△ PQS△

You Try!

•Classify XYZ as acute, equiangular, △obtuse, or right. Explain your reasoning.

•What about XWY? WYZ? △ △

Classifying Triangles by Sides

•1. Equilateral Triangle•2. Isosceles Triangle•3. Scalene Triangle

Equilateral Triangle

Equilateral Triangle

•Three Congruent Sides

Isosceles Triangle

Isosceles Triangle

• Two congruent sides

• PAUSE: This means what else can we call an equilateral triangle?

Scalene Triangle

Scalene Triangle

•No congruent sides

Example Three:

Example Four:

If point M is the midpoint of JL, classify JKM as equilateral, isosceles, or △

scalene. What about ? Explain your reasoning.

You Try!

If point Y is the midpoint of VX and WY = 3.0 units, classify VWY, △and as equilateral, isosceles, or scalene. Explain your reasoning.

Realize…. • You can double classify triangles– once by sides, once by

angles

• Example: is a __________ triangle

Example Five: Find the measures of the sides of isosceles triangle ABC△

You Try! • Find the measures of the sides of What type of triangle is

it?

Triangle Angle Sum Theorem • The sum of the measures of the angles in a triangle is 180

degrees.

How do we know!?!?!?• Let’s Prove it!

• Given: • Prove:

Example Six: • Find x, y, and z

Example Seven: • Find each of the number angles

You Try! Find the measure of each numbered angle.

Practice Problems

• Try some on your own/in small groups!• As always if you are confused/have questions don’t hesitate to call me over!

Exit Ticket: • Find x and then classify the triangle based on the angles.