1. Warm UP March 10, 2014 Classify each triangle by its angles and by its sides.
45° E F G
60° A B C

2. EOCT Week 9 #1

3. Parts of Isosceles Triangles
The angle formed by the congruent sides is called the vertex angle.
The two angles formed by the base and one of the congruent sides are called base angles.
The congruent sides are called legs.
leg
leg
base angle
base angle
The side opposite the vertex is the base.

4. Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent.
If , then

5. Converse of Base Angles Theorem
If two angles of a triangle are congruent, then the sides opposite them are congruent.
If , then

6. Apply the Base Angles Theorem
EXAMPLE 1
Apply the Base Angles Theorem
Find the measures of the angles.
SOLUTION Q P
Since a triangle has 180°, 180 – 30 = 150° for the other two angles.
Since the opposite sides are congruent, angles Q and P must be congruent.
150/2 = 75° each.
(30)° R

7. Apply the Base Angles Theorem
EXAMPLE 2
Apply the Base Angles Theorem
Find the measures of the angles. Q P
(48)° R

8. Apply the Base Angles Theorem
EXAMPLE 3
Apply the Base Angles Theorem
Find the measures of the angles. Q P
(62)° R

9. EXAMPLE 4
Apply the Base Angles Theorem
Find the value of x. Then find the measure of each angle. P
SOLUTION
(12x+20)°
Since there are two congruent sides, the angles opposite them must be congruent also. Therefore, 12x + 20 = 20x – 4
20 = 8x – 4
24 = 8x
3 = x
(20x-4)° Q R
Plugging back in,
And since there must be 180 degrees in the triangle,

10. Apply the Base Angles Theorem
EXAMPLE 5
Apply the Base Angles Theorem
Find the value of x. Then find the measure of each angle. Q P
(11x+8)°
(5x+50)° R

11. Apply the Base Angles Theorem
EXAMPLE 6
Apply the Base Angles Theorem
Find the value of x. Then find the length of the labeled sides.
SOLUTION Q P
(80)°
(80)°
Since there are two congruent sides, the angles opposite them must be congruent also. Therefore, 7x = 3x + 40
4x = 40
x = 10
3x+40 7x
Plugging back in,
QR = 7(10)= 70
PR = 3(10) + 40 = 70 R

12. Apply the Base Angles Theorem
EXAMPLE 7
Apply the Base Angles Theorem
Find the value of x. Then find the length of the labeled sides. P
(50)°
5x+3
(50)° R Q
10x – 2

13. Right Triangles
HYPOTENUSE
LEG
LEG

14. Exterior Angles
Interior Angles

15. x + y + z = 180° Triangle Sum Theorem
The measures of the three interior angles in a triangle add up to be 180º.
x + y + z = 180° x° y° z°

16. m T = 59º m R + m S + m T = 180º 54º + 67º + m T = 180º
54°
54º º + m T = 180º
121º + m T = 180º
67° S T
m T = 59º

17. y = 40º m  D + m DCE + m E = 180º 55º + 85º + y = 180ºB
55º + 85º + y = 180º y°
140º + y = 180º C x°
85°
y = 40º
55° D A

18. Find the value of each variable.x°
43° x°
57°
x = 50º

19. Find the value of each variable.
55°
(6x – 7)°
43°
(40 + y)°
28°
x = 22º
y = 57º

20. Find the value of each variable.
50°
53° x°
50°
62°
x = 65º

21. Exterior Angle Theorem
The measure of the exterior angle is equal to the sum of two nonadjacent interior angles 1
m1+m2 =m3 2 3

22. Ex. 1: Find x. B. A. 72 43
148 76 x x 38 81

23. Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are
complementary.
x + y = 90º x° y°

24. Find mA and mB in right triangle ABC.
mA + m B = 90
2x x = 90
2x°
5x = 90
x = 18
3x° C B
mA = 2x
mB = 3x
= 2(18)
= 3(18)
= 54
= 36

25. Homework:
Practice WS