1. OBJECTIVE: 7x – 50 = 3x + 2x + 10 7x – 50 = 5x + 10 2x = 60 x = 30
Given two triangles, students will determine whether the triangles are congruent using the Side-Side-Side postulate
7x – 50 = 3x + 2x + 10
7x – 50 = 5x + 10
2x = 60
x = 30

3. Essential Question Learning Objective
What are the shortcuts to knowing if two triangles are congruent?
Given triangles, I will explain whether they are congruent or not by SSS (side-side-side).

4. The Idea of a Congruence
Two geometric figures with exactly the same size and shape. A C B D E F

5. How much do you
need to know. . .
. . . about two triangles
to prove that they
are congruent?

6. These relationships help define the congruent triangles.
In the figure, ΔABC 
ΔFDE. A
As in a mapping, the order of the _______ indicates the corresponding parts.
vertices C B
Congruent Angles
Congruent Sides
A  F
AB  FD F E D
B  D
BC  DE
C  E
AC  FE
These relationships help define the congruent triangles.

7. Do you need all six ?
NO !

8. Side-Side-Side (SSS)
AB  DE
BC  EF
AC  DF
ABC   DEF B A C E D F

9. Triangles are congruent.
Postulate 19
SSS
Postulate
If three _____ of one triangle are congruent to _____ _____________ sides of another triangle, then the two
Triangles are congruent.
sides
three
corresponding A B C R S T
If AC 
RT and
AB 
RS and
BC  ST
then ΔABC
 ΔRST

10. Sample Answer: ΔZXY  ΔFDE
In two triangles, ZY  FE, XY  DE, and XZ  DF.
Write a congruence statement for the two triangles. X D Z Y F E
Sample Answer:
ΔZXY  ΔFDE

11. Pair Share
Is there enough information to prove the triangles are congruent?
YES NO
What else is needed?
All Sides 
RS  TV

12. Yes; RTRT by the Reflexive property so ∆RST∆RQT by SSS
Yes; BDDB by the Symmetric property so ∆ABD∆CDB by SSS
Yes; corresponding sides are congruent so ∆ABC∆DEF by SSS

13. ∆VWR is not a right triangle
SR = 3 and RT = 5
Use the distance formula or Pythagorean Theorem to find PR and ST.
∆VWR is not a right triangle
Check to see if PR  ST
ST =
PR =
∆PQR∆SRT
by SSS
HOUSTON, WE HAVE A PROBLEM!!

14. say

15. You try:
Why are they congruent? F D C A E B

16. This idea of triangles is used in engineering. Let’s see how

18. Exit Slips 2. 1. 3.

19. What Was the Objective for Today?
Students will use side lengths to prove triangles are congruent.
Mastery is 80% or better on 5-minute checks and practice problems.

20. Homework
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