Post on 21-Jan-2016
transcript
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.