Bell Work Find the measure of the missing variables and state what type of angle relationship they have(alt. interior, alt. ext, same side interior, corresponding). 1)2) 3)4)

Agenda BellWork Agenda Outcomes Notes 4.1 White Board Activity IP – 4.1 Worksheet

Outcomes I will be able to: 1) Classify a triangle by its sides and/or angles 2) Find the measure of interior angles of a triangle using the Triangle Sum Theorem 3) Find the exterior angles of a triangle using the Exterior Angle Theorem

Triangles What is a triangle? Triangle – A polygon formed by three segments joining three noncollinear points Example: There are two ways to classify triangle: 1) By its sides 2) By its angles

Names Of Triangles Classifications By Sides 1. Equilateral Triangles Example: What does it mean for a triangle to be equilateral? ***All sides must be congruent

Names of Triangles Classifications by Sides 2. Isosceles Triangle Example: What does it mean for a triangle to be isosceles? ***At least two sides are congruent ***So, an equilateral triangle is also isosceles

Names of Triangles Classification by Sides 3. Scalene Triangle Example: What does it mean for a triangle to be scalene? ***No sides are congruent

Classify the following Triangles 1) 2) 3) 4) 5) 6)

Names of Triangles Classification by Angles 4. Acute Triangle Example: What do you notice about all of the angles? ***An acute triangle has all acute angles

Names of Triangle Classifications by Angles 5. Equiangular Triangle Example: What do you notice about all of the angles? They are all congruent ***An equiangular triangle has all angles congruent ***An equiangular triangle is also acute.

Names of Triangles Classification by Angles 6. Right Triangle Example: What do you notice about the angles? There is one right angle ***There is one right angle in every right triangle

Names of Triangles Classification by Angles 7. Obtuse Triangles Example: What do you notice about the angles? ***There is one obtuse angle in every obtuse triangle

Classifying Triangles When classifying triangles, we can classify them by both their sides and their angles What type of triangle would this be? Right Isosceles Triangle or Isosceles Right Triangle We can name a triangle by angles or sides first

Classifying Triangles Examples How would you classify this triangle? Obtuse Scalene Triangle

Classifying Triangle Examples How would you classify this triangle? Acute Scalene Triangle

Parts of Triangles Vertex – Each point joining the sides of a triangle Example: A, B, and C are all vertices Adjacent Sides – The two sides sharing a vertex AC and AB, AB and BC, AC and BC are adjacent sides A B C

Parts of Triangles A B C The sides that form the right angle AB and BC are the legs of this triangle The side opposite the right angle hypotenuse leg

Parts of Triangles The non-congruent side of an isosceles triangle base The congruent sides of an isosceles triangle leg

Types of Angles in Triangles There are both interior and exterior angles we are concerned with when looking at triangles Interior angle are inside the triangle Exterior angles are outside the triangle

Triangle Sum We can conclude that all the angles add to 180° Think about the angle sums!!!

Triangle Sum Theorem

Exterior Angle Theorem We can conclude that the sum of the remote interior angle is equal to the exterior angle = Compare the inside angles to the outside angle

Exterior Angle Theorem

Examples How can we solve this? x = x = x = 48

Examples How can we solve this? x+ 110 = 4x – 7 -x -x 110 = 3x – = 3x 39 = x

Examples How can we solve this? Remember, we can label things we know even if they are not in our picture. Now we have, 33 + x + 90 = x = x = 57 90

Examples How can we solve this? x + x + 30 = 180 2x + 30 = x = 150 x = 75

Independent Practice 1) Solve for the missing variable 2) Circle the chart r = 180 r + 90 = 180 r = 90