1. 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)

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

3. 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

4. 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

5. 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

6. 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

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

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

9. 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

10. 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.

11. 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

12. 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

13. 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

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

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

16. 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

17. 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

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

19. 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

20. Triangle Sum We can conclude that all the angles add to 180° Think about the angle sums!!! 43 67 70 90 50 40

21. Triangle Sum Theorem

22. Exterior Angle Theorem We can conclude that the sum of the remote interior angle is equal to the exterior angle =120 80 40 90 60 30 Compare the inside angles to the outside angle

23. Exterior Angle Theorem

24. Examples How can we solve this? 42 + 90 + x = 180 132 + x = 180 -132 -132 x = 48

25. Examples How can we solve this? x+ 110 = 4x – 7 -x -x 110 = 3x – 7 +7 +7 117 = 3x 39 = x

26. 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 = 180 123 + x = 180 -123 -123 x = 57 90

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

28. Independent Practice 1) Solve for the missing variable 2) Circle the chart r + 53 + 37 = 180 r + 90 = 180 r = 90