1. Isosceles, Equilateral, and Right Triangles
Chapter 4.6

2. Isosceles Triangle Theorem
Isosceles   The 2 Base s are 
Base angles are the angles opposite the equal sides. 

3. Isosceles Triangle TheoremB
If AB  BC, then A  C

4. Isosceles Triangle TheoremB
If A  C then AB  BC

5. Sample Problem Solve for the variables mA = 32° mB = (4y)°
mC = (6x +2)° A C B
y = 180
4y + 64 = 180
4y = 116
y = 29
6x + 2 = 32
6x = 30
x = 5

6. Find the Measure of a Missing Angle
180o – 120o = 60o
180o – 30o = 150o
Lesson 6 Ex2

7. A. 25
B. 35
C. 50
D. 130 A B C D
Lesson 6 CYP2

8. A. Which statement correctly names two congruent angles?B. C. D. A B C D
Lesson 6 CYP3

9. B. Which statement correctly names two congruent segments?D. A B C D
Lesson 6 CYP3

10. Equilateral Triangle Theorem
Equilateral   Equiangular 
Each angle = 60o !!!

11. Use Properties of Equilateral Triangles
Linear pair Thm.
Substitution
Subtraction
Answer: 105
Lesson 6 Ex4

12. A. x = 15
B. x = 30
C. x = 60
D. x = 90 A B C D
Lesson 6 CYP4

13. A. 30
B. 60
C. 90
D. 120 A B C D
Lesson 6 CYP4

14. Don’t be an ASS!!! Angle Side Side does not work!!!
(Neither does ASS backward!)
It can not distinguish between the two different triangles shown below.
However, if the angle is a right angle, then they are no longer called sides. They are called…

15. Hypotenuse-Leg   Theorem
If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts in another right triangle, then the triangles are congruent.

16. ABC  XYZ Why? HL   Theorem

17. Prove XMZ  YMZ Given Given Reflexive ZMX  ZMY HL   Thm
Step
Reason X Y Z M
Given
Given
mZMX = mZMY = 90o
Def of  lines
Reflexive
ZMX  ZMY
HL   Thm

18. Corresponding Parts of Congruent Triangles are Congruent
Given ΔABC  ΔXYZ
You can state that:
A  X
B  Y
C  Z
AB  XY
BC  YZ
CA  ZX

19. Suppose you know that ABD  CDB by SAS   Thm
Suppose you know that ABD  CDB by SAS   Thm. Which additional pairs of sides and angles can be found congruent using Corr. Parts of  s are ?

20. Complete the following two-column proof.
Statements
Reasons 1.
1. Given 2.
2. Isosceles Δ Theorem 3.
3. Given 4.
4. Def. of midpoint
Lesson 6 CYP1

21. SAS   Thm. Corr. Parts of  s are 
Complete the following two-column proof.
Proof: 4.
Reasons
Statements
4. Def. of midpoint
5. ______ 6. ?
5. ΔABC ΔADC ? A B C D
SAS   Thm.
Corr. Parts of  s are 
Lesson 6 CYP1

22. Homework
Video C
Ch 4-6
pg 248
1 – 10, 14 – 27, 32, 33, 37 – 39, & 48
Reminder!
Midpoint Formula: