HONORS GEOMETRY 4.1. 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

Has 3 acute angles

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

One Obtuse Angle

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

Three Congruent Sides

Isosceles Triangle

Two congruent sides PAUSE: This means what else can we call an equilateral triangle?

Scalene Triangle

No congruent sides

Example Three:

Example Four:

You Try!

Realize….

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

You Try!

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

How do we know!?!?!?

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.