4.4 and 4.5 triangle congruence conjectures.web.cerritos.edu/dford/sitepages/fall2011/math70lecture...

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4.4 and 4.5 TRIANGLE CONGRUENCE CONJECTURES.

Ways to show two Triangles are Congruent:

Side-Side-Side Side-Side-Angle Side-Angle-Angle

Angle-Angle-Angle Angle-Side-Angle Side-Angle-Side

A C

C

A C

C

A

Construct a triangle, more than one if possible, using the following:

a) b) c)

Draw a triangle with the following interior angles 45, 45, 90.

Why did SSA not work?

Why did AAA not work?

A B

A C

B C

A B

3

Mark the following triangles given the stated congruent triangle conjecture.

DEF

SSS SAA

ASA SAS

Determine which triangles are congruent and why?

Using your previous conjectures mark congruent angles and sides if they exist and then find the corresponding congruent triangle. State the reason the two triangles are congruent.

A

B C

E

D F

A

B C

E

D F

A

B C

E

D F

A

B C

E

D F

1 OHW ___________

Which conjecture supports the congruence statement?(if not enough info, write not enough info) _________

2. sAB // sCD ( hint: transversal?), sAD sBC , ABC ___________

Which conjecture supports the congruence statement?(if not enough info, write not enough

info) _________

3. sAC sBD, sAD sBC, ADB ___________

Which conjecture supports the congruence statement? _________

a a

A B

C D

a a

A

C

E

D

B

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5. sQD sAD, sQU sAU If you construct segment DU, you can show QDU ADU.

Which conjecture tells you they are congruent? ______

6. sAB sCD, CDB ABD

Which conjecture tells you that ABD CDB? _________

a a

Q

A

D

U

a a

A C

E

D B

10. which conjecture supports each congruence statement?

ABH CBD _________

HGF DEF _________

HFB DFB _________

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a a

P R

S

Review:

Construct the ABC so that it is congruent to PSR using ASA

Construct the ABC so that it is congruent to PSR using SSS

Construct the ABC so that it is congruent to PSR using SAS

4.6 CPCTC 1. ABC _______. Which conjecture supports the congruence statement? _________

A B

D

C

Because of ___________ both triangles are congruent. Which means

BDCCABandBCACBDsDBsAC ,,

CPCTC ----- Corresponding Parts of Congruent Triangles are Congruent

2. ABC _______

Which conjecture supports the congruence statement? __________

A

B

C E

D

Because of ___________ both triangles are congruent. Which means

BCADCEandDBsDCsBCsEDsAB ,,,

3. sAB sCD, sAB sCD, EC sCD, A D, ABC _______

Which conjecture supports the congruence statement? _________

Because of ___________ both triangles are congruent. Which sides and angles are congruent?

a a

A B

C

D

E

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H

R

GIVEN

GIVEN

KO

4.7 FLOWCHART THINKING

1. Provide each missing reason or statement in the flow-chart proof.

Given: sHR sSE

R S

Show: sHU sEU

S

Flow-chart Proof: E U

5. From the picture fill in the given and

Prove: KO

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GIVEN

GIVEN

GIVEN

GIVEN

GIVEN

GIVEN

6. Find the two congruent triangles and draw them next to each other, then write a proof.

Given: sPR sPQ

sPT sPS

Prove: PRT PQS

7. From the picture fill in the given and

Prove: sYWsOW

8. Given: D C

sDE sEC

Prove: sAE sBE