Steps for triangle congruence proofs - COACH PHILLIPS

[Pages:11]Geometry Support

Unit 2--Triangle Congruence

Name:

Proving Triangles Congruent NOTES

From yesterday, you learned that you only need 3 pieces of information (combination of angles and sides) to determine if two triangles are congruent. Today, we are going to prove two triangles are congruent using two column proofs.

Steps for triangle congruence proofs:

1. Write the `givens.' 2. If your given is not already a ____________________________________, use it to get to one.

(Think...what does that given mean? What is the definition of that word?) 3. Once you have gotten down to congruence statements, check your triangles to see if

you have enough information (3 pieces) to prove that they are __________________. a. If you do not have enough information, see if you can add _______________________________ or __________________________________________.

4. State that the triangles are congruent and provide the reason (ASA, SAS, SSS, AAS, HL).

********And always remember...IF YOU WRITE IT, MARK IT!!!!**********

Practice:

1. Given: BC DC and AC EC Prove: BCA DCE

Statement

1.

1.

2.

2.

3.

3.

4.

4.

Reason

Geometry Support

Unit 2--Triangle Congruence

Common Statements You Will See/Use in Proofs:

If....

Then...

P is the midpoint of AE

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Because...

TU bisects STG . ED XY

XF GH GTS is isosceles with legs TG and TS.

Geometry Support

Unit 2--Triangle Congruence

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2. Given:, AY BY, AYX BYZ, and Y is the midpoint of XZ Prove: XYA ZYB

Statement

1.

1.

2.

2.

3.

3.

4.

4.

5.

5.

Reason

3. Given: RTS is isosceles with legs RT and TS. Q is the midpoint of RS.

Prove: RTQ STQ

Statement

1.

1.

Reason

2.

2.

3.

3.

4.

4.

5.

5.

6.

6.

4. Given: P N and M is the midpoint of PN. Prove: PMK NQM

Statement

1.

1.

2.

2.

3.

3.

4.

4.

5.

5.

Reason

Geometry Support

Unit 2--Triangle Congruence

5. Given: AC BD and AD BC Prove: ABD BAC

Statement 1. AC BD 2. AD BC 3. AB AB 4. ABD BAC

1. Given

Reason

2. Given

3. Reflective Property

4.Side-Side-Side (SSS)

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6. Given: GH IH and GF IH Prove: ABD BAC

Statement

1.

1.

2.

2.

3.

3.

4.

4.

Reason

7. Given: SR TU and S U Prove: SRT UTR

Statement

1.

1.

2.

2.

3.

3.

4.

4.

5.

5.

Reason

Geometry Support

Unit 2--Triangle Congruence

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Name __________________________________ Date _____________

Triangle Congruence Proofs Practice

1. Given: C is the midpoint of BE AND AD. Prove: ABC DEC

Statement

1. C is midpoint of BE and AD 1.

Reason

2. BC EC

2. definition of a midpoint

3.

3. definition of a midpoint

4.

4.

5. ABC DEC

5.

2. Given: BC DA and AC bisects BCD Prove: ABC CDA

Statement 1. 2. AC bisects BCD

3. ________ ________ 4. AC AC

5.

1. 2. Given 3. 4. 5.

Reason

3. Given: X H and XG FH Prove: XGF HFG

Statement 1. 2.

3. FGX GFH

4. 5.

1. Given 2. Given 3. 4. 5.

Reason

Geometry Support

Unit 2--Triangle Congruence

Name:

Name ____________________________ Date ___________

Triangle Congruence Proofs Practice Continued

Matching: Use the choices listed at the bottom in the box for problems #1 ? 4

Problem 1:

Statement 1. LM LO 2. MN ON 3. LN LN

1. Given 2. Give n 3.

Reason

4. LMN LON 4.

Problem 2:

Statement

1. QS || RT 2. R S 3. 1 2

4. QT QT

5. QST TRQ

1. Given 2. Given 3.

4.

5.

Reason

Problem 3:

Statement 1. GI KI 2. HI JI

3. GIH KIJ

4. GIH KIJ

1. Given 2. Given 3.

4.

Reason

Problem 4:

Statement

1. AC || BD, AB || CD 2. 1 4, 2 3

3. AD AD 4. ADC DAB

1. Given 2. 3. 4.

Reason

Choices for problems #1 ? 4 (some will be used more than once): AAS ASA

Alternate Interior Angles Reflexive Property SAS SSS Vertical Angles

Geometry Support Fill in the blank proofs: Problem 5:

Problem 6:

Unit 2--Triangle Congruence

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Statement

1. I K 2. IHJ KJH

3. HJ HJ 4. HJK JHI

1. Given 2. Given 3.

4.

Reason

Statement

1. MLN ONL 2. OLN _____

3.

4. LNO NLM

1. Given 2. Given

Reason

3. Reflexive Property 4.

Problem 7: Problem 8:

Statement

R

1. PQ QS

1. Given

2.

3. PQT RQS

2. Given 3.

4. PQT SQR 4.

Reason

Statement

1. UV UX 2. VWU XWU 3. 4. V X 5. UWV UWX

1. Given

Reason

2. Given 3. Reflexive Property 4. 5..

Problem 9:

Statement

1. Y C

2. 3.

4. YZA CBA

Reason 1.

2. Given 3. Vertical Angles are 4.

Geometry Support Create your own!

A. Given: AB CD, BC AD

Prove: ABC CDA ?

Unit 2--Triangle Congruence

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Given : AB CD and AE CE

B.

Pr ove : ABE CDE?

Given : AB BD C. BCA and BCD are right angles

Pr ove : ABC DBC?

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