Use ASA to Prove Triangles Congruent

Write a two-column proof.

Use ASA to Prove Triangles Congruent

4. Alternate Interior Angles4. W E

Proof:Statements Reasons

1. Given1. L is the midpoint of WE.____

3. Given3.

2. Midpoint Theorem2.

5. Vertical Angles Theorem5. WLR ELD

6. ASA6. ΔWRL ΔEDL

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 hypotenuseand corresponding legs. Hence, HL.

Example 4: Determine whether each pair of triangles is congruent. If yes, state the postulate/theorem that applies.

4. 5. 6.

Each triangle has right angles that are congruent, a 2nd set of corresponding angles that are congruent, and a side in between the 2 angles that is congruent. ASA

Each triangle has right angles that are congruent, a 2nd set of corresponding angles that are congruent, and a 3rd set of corresponding angles that are congruent.NOT POSSIBLE.(AAA does not exist)

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.

Prove: ΔABC ΔDCB

Given: AB BC, DC BC, AC BD

Proof:ReasonsStatements

1. 2.3. Given 4. Definition of 5. 6. Reflexive Property7.

GivenDefinition of

ΔABC ΔDCBHL

Given

 

 

DCB is a right angle

 

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

A. SSS

B. ASA

C. SAS

D. not possible

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4

A. SSS

B. ASA

C. SAS

D. not possible

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4

A. SAS

B. AAS

C. SSS

D. not possible

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4

A. SSA

B. ASA

C. SSS

D. not possible

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4

A. AAA

B. SAS

C. SSS

D. not possible

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4

Given A R, what sides must you know to be congruent to prove ΔABC ΔRST by SAS?

A.

B.

C.

D.

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