Use ASA to Prove Triangles Congruent
Write a two-column proof.

Use ASA to Prove Triangles Congruent
Proof:
Statements Reasons
1.
L is the midpoint of
WE.
2.
1.
Given
2.
Midpoint Theorem
3.
4.

W
 
E
5.

WLR
 
ELD
6.
Δ WRL
 Δ EDL
3.
4.
5.
6.
Given
Alternate Interior Angles
Vertical Angles Theorem
ASA

Use AAS to Prove Triangles Congruent
Write a paragraph proof.

Apply Triangle Congruence
MANUFACTURING Barbara designs a paper template for a certain envelope. She designs the top and bottom flaps to be isosceles triangles that have congruent bases and base angles. If EV = 8 cm and the height of the isosceles triangle is 3 cm, find PO.

Proving RIGHT TRIANGLES congruent
*As long as statement(s) mention right angles , you only need 2 congruent pieces in each triangle: each hypotenuse and corresponding legs . Hence, HL .

Example 4: Determine whether each pair of triangles is congruent.
If yes, state the postulate/theorem that applies .
4.
Each triangle has right angles that are congruent, a
2 nd set of corresponding angles that are congruent, and a side in between the 2 angles that is congruent.
ASA
5.
Each triangle has right angles that are congruent, a 2 nd set of corresponding angles that are congruent, and a 3 rd set of corresponding angles that are congruent.
NOT POSSIBLE.
(AAA does not exist)
6.
Each triangle has right angles that are congruent, a set of corresponding sides that are congruent, and share a side, but SSA does not exist. (the angle is not the included angle).
However, because the triangles are right triangles, they share the hypotenuse, and have a set of congruent legs. HL

Example 5: Complete the proof.
Given: AB

BC , DC

BC, AC

BD
Prove: Δ ABC
 Δ DCB
Proof:
Statements Reasons

DCB is a right angle
1.
2.
Given
Definition of

3. Given
4. Definition of

5. Given
6. Reflexive Property
7.
HL
Δ ABC
 Δ DCB

Five-Minute Check (over Lesson 4 –4)
CCSS
Then/Now
New Vocabulary
Postulate 4.3: Angle-Side-Angle (ASA) Congruence
Example 1: Use ASA to Prove Triangles Congruent
Theorem 4.5: Angle-Angle-Side (AAS) Congruence
Example 2: Use AAS to Prove Triangles Congruent
Example 3: Real-World Example: Apply Triangle Congruence
Concept Summary: Proving Triangles Congruent

Over Lesson 4 –4
Determine which postulate can be used to prove that the triangles are congruent.
If it is not possible to prove congruence, choose not
possible.
A.
SSS
B.
ASA
C.
SAS
D.
not possible

Over Lesson 4 –4
Determine which postulate can be used to prove that the triangles are congruent.
If it is not possible to prove congruence, choose not
possible.
A.
SSS
B.
ASA
C.
SAS
D.
not possible

Over Lesson 4 –4
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not
possible.
A.
SAS
B.
AAS
C.
SSS
D.
not possible

Over Lesson 4 –4
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not
possible.
A.
SSA
B.
ASA
C.
SSS
D.
not possible

Over Lesson 4 –4
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not
possible.
A.
AAA
B.
SAS
C.
SSS
D.
not possible

A.
B.
C.
D.
Over Lesson 4 –4
Given

A
 
R, what sides must you know to be congruent to prove ΔABC  ΔRST by SAS?

Content Standards
G.CO.10 Prove theorems about triangles.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Mathematical Practices
3 Construct viable arguments and critique the reasoning of others.
5 Use appropriate tools strategically.

You proved triangles congruent using SSS and
SAS.
• Use the ASA Postulate to test for congruence.
• Use the AAS Theorem to test for congruence.

• included side