1. Notes Lesson 5.2
Congruent Triangles
Target 4.1

2. What information is sufficient to prove triangles congruent?
Congruent Figures
Lesson 5.2
Definition:
Congruent triangles are triangles that have all corresponding sides congruent and all corresponding angles congruent.
Write a congruence statement for the triangles at the left.
What information is sufficient to prove triangles congruent?

3. Find the value of x and the lengths of the given sides.
Congruent Figures
Target 4.1
Example 2:
XYZ KLM,
YZ= x + 10
LM= 2x
Find the value of x and the lengths of the given sides.
Begin marking these triangles with corresponding angles that are congruent.

4. Leading to Target 4.2

7. Triangle Congruence by SSS and SAS
Lesson 5.3

8. Write a two-column proof.
Triangle Congruence by ASA and AAS
Example 3:
Write a two-column proof.
Given: A B, AP BP
Prove: APX BPY 1 2 1 2
Statements Reasons
Given
Vertical angles are congruent.
ASA

9. Write a two-column proof that uses AAS. Given: B D, AB || CD
Triangle Congruence by ASA and AAS
Example 4:
TARGET 4.3 & 4.5
Given 2
Not an included side 1
Write a two-column proof that uses AAS.
Given: B D, AB || CD
Prove: ABC CDA
Statements Reasons
1. B D, AB || CD 1. Given
2. 1 2 2. If lines are ||, then alternate interior angles are .
3. AC CA 3. Reflexive Property of Congruence
4. ABC CDA 4. AAS Theorem

10. Triangle Congruence by SSS and SAS
Target 4.2
Example 5:
Copy the diagram.
Mark the congruent sides.
Given: M is the midpoint of XY, AX AY
Prove: AMX AMY
From the given information, can you prove that the triangles are congruent. Explain.
Midpoint M implies MX MY. AM AM by the Reflexive Property of Congruence AMX AMY by the
SSS Postulate.

11. a) Draw the two congruent triangles separately.
Triangle Congruence by SSS and SAS
Target 4.2
Example 6: A B
a) Draw the two congruent triangles separately. a) D C C D b)
DC CD by the Reflexive Property.
You now have two pairs of corresponding congruent sides.
Therefore if you know ADC BCD,
you can prove
ADC BCD by SAS.
b) AD BC. What other information do you need to prove ADC BCD by SAS?
Edit text. See page 62.
GEOM_3eTP04_58-74_MQ

12. TARGET 4.3
YOU TRY #1 A

13. Review: Right triangle:
Hypotenuse
Leg H L L
Leg
TARGET 4.4

14. What additional information is needed to prove. Prove: ABC DCB by HL.
Congruence in Right Triangles
TARGET 4.4
Example 7:
What additional information
is needed to prove.
Prove: ABC DCB
by HL. C C D B A B
Since BC CB Reflexive Property of Congruence
You must prove that BD CA
To prove ABC DCB by the (HL Theorem).

15. Congruence in Right Triangles
TARGET 4.4
Example 8:
One student wrote “ CPA MPA
by SAS” for the diagram below.
Is the student correct? Explain.
The diagram shows the following congruent parts.
CA MA
CPA MPA
PA PA
The congruent angles are not included between the corresponding congruent sides.
The triangles are not congruent by the SAS Postulate, but they are congruent by the HL Theorem.

16. YOU TRY #2
TARGET 4.4
What additional information will allow you to prove the triangles congruent by the HL theorem? C

17. YOU TRY #3
TARGET 4.4 C