4.7

How Do You Prove Triangles Congruent?

Pg. 28

SSS≅, SAS≅, and HL≅ Proofs

4.7 – How Do You Prove Triangles Congruent?SSS≅, SAS≅, and HL≅ Proofs

Now that you have shortcuts for establishing triangle congruence, how can you organize information in a flowchart to show that triangles are congruent? Consider this as you work today with your team.

4.48 – HIDDEN STATEMENTSSometimes a proof needs a statement that is not given. Find each hidden fact in the pictures below.

alternate interior angles

vertical angles

reflexiveproperty

4.49 – STATE YOUR REASONFor each picture below, determine if the triangles are similar, congruent, or neither. If they are, write a similarity or congruence statement. Then state your reason. Be sure to mark any hidden facts in the picture. If they are not, explain why not.

SSS SAS

ASA AAS

ASS…..Not congruent AAS

SAS AA~

AAS

HL

4.50 – TRIANGLE CONGRUENCE Complete the following proofs. Make sure you MARK your picture!

1. AB AD 1. given

2. BC DC 2. given

3. AC AC 3. reflexive prop.

4. ABC ADC 4. SSS

1. bisects AC DB 1. given

2. DC CB 2. def. segment bisector

3. AD AB 3. given

4. AC AC 4. reflexive prop.

5. ACD ACB 5. SSS

b.

1. bisects AC DAB 1. given2. DAC BAC 2. def. angle bisector

3. DA BA 3. given

4. AC AC 4. reflexive prop.

5. ACD ACB 5. SAS

c.

2. DC CA 2. def. midpoint

3. EC BC 3. given4. ECD BCA 4. vertical s

1. is midpt. C AD 1. given

5. EDC BAC 5. SAS

d.

1. //AB DC 1. given2. BAC DCA 2. alternate interior s

3. DC BA 3. given

4. AC AC 4. reflexive prop.

5. ABC CDA 5. SAS

e.

1. AC DB 1. given2. DCA BCA 2. def. of lines3. AD AB 3. given

4. AC AC 4. reflexive prop.

5. ADC ACB 5. HL

f.