1. 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.

2. 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. b.
SOLUTION a.
From the diagram you know that AB  CB and DB  DB.
The angle included between AB and DB is ABD.
The angle included between CB and DB is CBD.
Because the included angles are congruent, you can use the SAS Congruence Postulate to conclude that ∆ABD  ∆CBD.

3. Example 2
Use the SAS Congruence Postulate b.
You know that GF  GH and GE  GE. However, the congruent angles are not included between the congruent sides, so you cannot use the SAS Congruence Postulate.

4. 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
The proof can be set up in two columns. The proof begins with the given information and ends with the statement you are trying to prove.

5. Example 3 Statements Reasons Given Given 3.
Write a Proof
These are the given
statements.
Statements
Reasons
Given 1.
JL  NL
Given 2.
L is the
midpoint of KM.
This information is from the diagram.
JKL  NML 3.
Vertical
Angles
Theorem

6. Example 3 Statements Reasons 5.
Write a Proof
Statement 4 follows from Statement 2.
Definition of
midpoint 4.
KL  ML
Statements
Reasons
∆JKL  ∆NML 5.
Statement 5 follows from the congruences of Statements 1, 3, and 4.
SAS Congruence
Postulate

7. Make a diagram and label it with the given information.
Example 4
Prove Triangles are Congruent
You are making a model of the window shown in the figure. You know that and  Write a proof to show that ∆DRA  ∆DRG. RG RA AG DR A D G R 
SOLUTION 1.
Make a diagram and label it with
the given information.

8. Write the given information and the statement you need to prove.
Example 4
Prove Triangles are Congruent 2.
Write the given information and the statement you need to prove.
∆DRA  ∆DRG
DR AG, RA  RG 
Write a two-column proof. List the given statements first. 3. 8

9. DRA and DRG are right angles. lines form right angles. 
Example 4
Prove Triangles are Congruent
Statements
Reasons 1.
RA  RG
Given 2.
DR AG 
Given 3.
DRA and DRG are right angles.
lines form right angles.  4.
DRA  DRG
Right angles are congruent. 5.
DR  DR
Reflexive Property of Congruence 6.
∆DRA  ∆DRG
SAS Congruence Postulate 9

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