1. Warm Up On Desk (5 min) Do Daily Quiz 5.1 (10 min)

2. Review
-go over the Daily Quiz
items in 5.1

3. 5.2
ESSENTIAL OBJECTIVE
Show triangles are congruent using SSS and SAS.

4. In Exercises 1–5, use the triangles below.
Determine whether the given angles or sides represent corresponding angles, corresponding sides, or neither. 1.
B and H
ANSWER
Corresponding angles 2.
DB and HK
ANSWER
neither

5. Complete the statement with the corresponding
congruent part. 3.
J  _____ ?
ANSWER D 4.
CB  _____ ?
ANSWER KH
The triangles are congruent. Identify all pairs of corresponding congruent parts. Then write a congruence statement. 5.
ANSWER
B  H, D  J, C  K, BD  HJ, BC  HK, CD  KJ; ∆BCD  ∆HKJ

6. 5.2

7. VOCABULARY
A proof is a convincing argument that shows why a statement is true.

8. Side-Side-Side Congruence Postulate (SSS)
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

9. Does the diagram give enough information to show that the
Example 1
Use the SSS Congruence Postulate
Does the diagram give enough
information to show that the
triangles are congruent? Explain.
SOLUTION
From the diagram you know that HJ  LJ and HK  LK.
By the Reflexive Property, you know that JK  JK.
ANSWER
Yes, enough information is given. Because corresponding sides are congruent, you can use the SSS Congruence Postulate to conclude that ∆HJK  ∆LJK. 9

10. Side-Angle-Side Congruence Postulate (SAS)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

13. From the diagram you know that AB  CB and DB  DB.
Example 2
Use the SAS Congruence Postulate
Does the diagram give enough information to use the SAS Congruence Postulate? Explain your reasoning. a.
SOLUTION a.
From the diagram you know that AB  CB and DB  DB.
angle ABD and
angle CBD are  (coz both are 90)
Yes, we can use the SAS Congruence Postulate to conclude that ∆ABD  ∆CBD.

14. No, we cannot use the SAS Congruence Postulate.
Example 2
Use the SAS Congruence Postulate b.
You know that GF  GH and GE  GE. However, it does not follow the SAS congruence postulate. So,
No, we cannot use the SAS Congruence Postulate.

15. Introducing: Two Column Proof

17. Write a two-column proof that shows ∆JKL  ∆NML.
Example 3
Write a Proof
Write a two-column proof that shows ∆JKL  ∆NML.
∆JKL  ∆NML
JL  NL
L is the midpoint of KM.
SOLUTION
To set up the two column proof, start with the given:

18. Example 3 Statements Reasons Given Given 4.
Write a Proof
(Side)
Statements
Reasons
Given 1.
JL  NL
Given 2.
L is the
midpoint of KM.
3. Definition of
midpoint
3. KL  ML
(An included angle!)
JLK  NLM 4.
Vertical
Angles
Theorem

19. Example 3 Statements Reasons Given Given 4. 5.
Write a Proof
Side
side
Statements
Reasons
Given 1.
JL  NL
Given 2.
L is the
midpoint of KM.
3. Definition of
midpoint
3. KL  ML
An included angle
JKL  NML 4.
Vertical
Angles
Theorem
∆JKL  ∆NML 5.
SAS Congruence
Postulate

20. proof to show that ∆DRA  ∆DRG.
Example 4 A D G R  RG RA AG DR
From the figure,
and 
proof to show that ∆DRA  ∆DRG.
. Write a
SOLUTION 1.
Make a diagram and label it with
the given information.

21. Checkpoint Example. ∆BCA  ∆ECD DC AC  CB  CE , CB  CE Statements
Prove Triangles are Congruent
Example.
∆BCA  ∆ECD DC
AC 
CB  CE ,
CB  CE
Statements
Reasons 1. ?
_____
ANSWER
Given 2. ?
_____
ANSWER
BCA  ECD 3. ?
_____
ANSWER
∆BCA  ∆ECD 4. ?
_____
ANSWER

22. DRA and DRG are right angles. lines form right angles. 
Example 4
Prove Triangles are Congruent
Statements
Reasons 1.
RA  RG
Given
side 2.
DR AG 
Given 3.
DRA and DRG are right angles.
lines form right angles.  4.
DRA  DRG
Right angles are congruent.
angle 5.
DR  DR
Reflexive Property of Congruence
side 6.
∆DRA  ∆DRG
SAS Congruence Postulate 22

23. Checkpoint Fill in. ∆BCA  ∆ECD DC AC  CB  CE , CB  CE Statements
Prove Triangles are Congruent
Fill in.
∆BCA  ∆ECD DC
AC 
CB  CE ,
CB  CE
Statements
Reasons 1. ?
_____
Given
ANSWER
Given 2. ?
_____ DC
AC 
ANSWER
Vertical Angles
Theorem
ANSWER
BCA  ECD 3. ?
_____
SAS
Congruence
Postulate
ANSWER
∆BCA  ∆ECD 4. ?
_____ 23

24. Hw 5.2A