1. TRIANGLE CONGRUENCE p q r a b c
LESSON 17

2. EXPLORING CONGRUENT TRIANGLES
Goal 1: How to identify congruent triangles.
Goal 2: How to identify different types of triangles .
Definition of Congruent Triangles
If ABC is congruent to PQR, then there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent. The notation ABC  PQR indicates the congruence. a b c p q r

3. at least two congruent sides
Classification of Triangles
By Sides
isosceles triangle
at least two congruent sides
scalene triangle
no congruent sides
equilateral triangle
three congruent sides

4. three congruent angles
Classification of Triangles
By Angles
obtuse triangle
one obtuse angle
acute triangle
three acute angles
Equiangular
three congruent angles
right triangle
one right angle

5. Congruence Again
The congruence symbol ““ has a different meaning than the equal symbol “=“. In geometry “=“ means “identical to” or “exactly the same as,” but ““ means that the measure (a number value) of two distinct objects of the same class is the same, or that the measure of the corresponding parts of the two objects is the same.

6. CONGRUENT POSTULATES
RECALL: Congruent triangles have 3 pairs of  angles and 3 pairs of  sides.
Do we want to show that all three pairs of angles are congruent and that all three pairs of sides are congruent every time?
YES!!!
You can construct congruent triangles with a minimum amount of information using the congruent postulates.

7. CONGRUENT POSTULATES:
SSS
Side-Side-Side (SSS) Postulate:
If all three pairs of corresponding sides of two triangles are equal, the two triangles are congruent.
If you know: then you know: and you know:
AB = DE
BC = EF
AC = DF
A =  D
B =  E
C =  F

8. CONGRUENT POSTULATES:
SSS
Side-Side-Side (SSS) Postulate:
AB = DE
BC = EF
AC = DF
A =  D
B =  E
C =  F

9. CONGRUENT POSTULATES:
SAS
Side-Angle-Side (SAS) Postulate:
If two pairs of corresponding sides and the corresponding contained angles of two triangles are equal, the two triangles are congruent.
If you know: then you know: and you know:
AB = DE
 B =  E
AC = DF
A =  D
BC = EF
C =  F

10. CONGRUENT POSTULATES:
SAS
Side-Angle-Side (SAS) Postulate:
A =  D
BC = EF
C =  F
AB = DE
 B =  E
AC = DF

11. CONGRUENT POSTULATES:
ASA
Angle-Side-Angle (ASA) Postulate:
If two angles and the contained side of one triangle are equal to two angles and the contained side of another triangle, the two triangles are congruent.
If you know: then you know: and you know:
 A =  D
 B =  E
AB = DE
AC = DF
C =  F
BC = EF

12. CONGRUENT POSTULATES:
ASA
Angle-Side-Angle (ASA) Postulate:
 A =  D
 B =  E
AB = DE
AC = DF
C =  F
BC = EF

13. CONGRUENT POSTULATES:
RHS
Right angle - Hypotenuse-Side (RHS) Postulate:
If the hypotenuse and another side of one right triangle are equal to the hypotenuse and one side of a second right triangle, the two triangles are congruent.
If you know: then you know: and you know:
 A =  D = 90o
BC = EF
AC = DF
B =  E
C =  F
AB = DE

14. CONGRUENT POSTULATES:
RHS
Right angle - Hypotenuse-Side (RHS) Postulate:
 A =  D = 90o
BC = EF
AC = DF
B =  E
C =  F
AB = DE

15. PROPERTIES OF CONGRUENT TRIANGLES REFLEXIVE
Every triangle is congruent to itself.
2. SYMMETRIC
If ABC  PQR, then PQR  ABC
3. TRANSITIVE
If ABC  PQR and PQR  TUV, then ABC  TUV

16. CLASS WORK Check solutions to lesson 16(3) Copy notes from Lesson 17
Do Lesson 17 worksheet