1. 3.4 & 4.5 Triangles

2. 3-4 Parallel Lines and the Triangle Angle-Sum Theorem
Objectives: 1) to classify triangles and find the measures of their angles
2) To use exterior angles of triangles

3. Watch the Video for the
Proof of Triangle Angle-Sum Theorem

4. Example 1: Find the values of x, y, and z.

5. You try. Find the values of x, y, and z.

6. You can classify a triangle by its angles and sides.

7. Try these. Draw and mark a triangle to fit each description
Try these. Draw and mark a triangle to fit each description. If no triangle can be drawn, write not possible and explain why.
acute scalene
Isosceles right
Obtuse equiangular

8. Exterior angle of a polygon: angle formed by a side and an extension of an adjacent side
Remote interior angles: the two nonadjacent interior angles

9. Proof of Triangle Exterior Angle Theorem

10. Example 3: Find each missing angle.

11. Try this. Find the measure of angle 1. 125=90+m∠1 35=m∠1

12. Try this one too.

13. Example 4: Find the value of x.

16. 4-5 Isosceles and Equilateral Triangles
Objective: use and apply properties of isosceles triangles

17. What is an Isosceles Triangle?
Isosceles triangle: A triangle with at least two congruent sides
Legs: The congruent sides of an isosceles triangle
Base: The “other” side not counting as the two congruent sides
Vertex angle: The angle included by the two congruent sides
Base angles: The Angles that include the Base

19. Example 5: Solve for Variable

20. c) d)

22. Try these.

23. Example 6: Apply Concepts
Triangle RST is an isosceles triangle.
R is the vertex angle, RS = x + 7, ST = x – 1, and RT = 3x – 5.
Find x, RS, ST, and RT.

24. Corollary: statement that follows directly from a theorem

25. Example 7: Solve for each variable.

26. Try these.