1. By Angle Measures By Side Lengths
Warm-up
1. How many degrees are in a triangle?
2. Classify the different types of triangles
By Angle Measures By Side Lengths

4. Triangle Sum Theorem:
The sum of the measures of the angles of a triangle is 180°.
m<A + m<B + m<C = 180°. A C B

5. Example 1:
Ex. 1 Find the m < Z
m < Z = 65

6. Example 2:
Find the values of a, b, and c.
a = 700
b = 200
c = 200

7. Example 3: Solve for x x°

8. Isosceles Triangle Sum Theorem
As isosceles triangle has two congruent sides. Theorem: If two sides of a triangle are congruent, the angles opposite them are congruent.

9. Example: Solve for x.

10. Example: Solve for angle measures 1, 2, 3 and 4.

11. Midsegment
A midsegment of a triangle is a segment that connects the midpoints of 2 sides of the triangle. Every triangle has 3 midsegments.

12. Midsegment Theorem
The segment connecting the midpoints of 2 sides of a triangle is parallel to the third side and is half as long as that side.
DE = ½ AC

13. Find the value of x
x = 3
x = 4

14. Given that DE is the midsegment and the given condition, solve for x: 1) AD = 2x-4 DB = 3x-8 2) AB = 6x-12 DB = 4x – 28 3) AE = 9x + 12 AC = 20x – 15 4) DE = BC = 4x - 3

15. Give it a try…
X is the midpoint of MN, Y is the midpoint of NO, and Z is the midpoint of MO.
a. Find XZ.
XZ = 9
b. If XY = 10, find MO.
MO = 20

16. In triangle ACE, B is the midpoint of
AC and D is the midpoint of CE.
Find the value of x if
a. AB = 4x – 5 and AC = 3x + 15
b. CD = 6x – 4 and DE = 4x + 8