# Geometry Notes 3.1 - Congruent Triangles by cometjunkie43

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```									Geometry Notes 3.1 – Congruent Triangles
1. Congruent Triangles

Reminder: the word “Congruent” means

Def’n: Two triangles are congruent when

Ex) Name and mark the corresponding congruent parts if ∆ABC ≅ ∆XYZ .
B

Y
C
A

Z                            X

Ex) Name the corresponding congruent parts if ∆ABC ≅ ∆ADE .

B                                        D

A
1       2

C                        E

Ex) Name the corresponding congruent parts (without a diagram) if ∆PQR ≅ ∆TWV .

30 Notes 3.1, Page 1 of 5
L. Morvan, Cypress College
2. SSS Method for proving congruent triangles

SSS:

Ex) Write the proof.                                                          A

C is the midpoint of DB

D                                   B
C

Statements (specific)                                Reasons (general)

1. ____________________________                1. ___________________________________________

2. ____________________________                2. ___________________________________________

3. ____________________________                3. ___________________________________________

4. ____________________________                4. ___________________________________________

Ex) Write the proof.                                          X                       Y

Given:    XW ≅ YZ , XZ ≅ YW

Prove: ∆XZW ≅ ∆YWZ
W                                   Z
Statements (specific)                                Reasons (general)

1. ____________________________                1. ___________________________________________

2. ____________________________                2. ___________________________________________

3. ____________________________                3. ___________________________________________

(hint: try drawing the triangles separately)

30 Notes 3.1, Page 2 of 5
L. Morvan, Cypress College
3. SAS Method for proving congruent triangles

SAS:

Ex) Write the proof.                                                                 D
B

Given:   BE and AD bisect each other                          C
1       2
Prove: ∆ABC ≅ ∆DEC
A
E
Statements (specific)                          Reasons (general)

1. ____________________________         1. ___________________________________________

2. ____________________________         2. ___________________________________________

3. ____________________________         3. ___________________________________________

4. ____________________________         4. ___________________________________________

A
Ex) Write the proof.

AC bisects ∠DAB
D                                    B
C

Statements (specific)                          Reasons (general)

1. ____________________________         1. ___________________________________________

2. ____________________________         2. ___________________________________________

3. ____________________________         3. ___________________________________________

4. ____________________________         4. ___________________________________________

30 Notes 3.1, Page 3 of 5
L. Morvan, Cypress College
4. ASA Method for proving congruent triangles

ASA:

Ex) Write the proof.                                                            D
B
Given: ∠A ≅ ∠D                                             C

Prove: ∆ABC ≅ ∆DEC                    A
E

Statements (specific)                       Reasons (general)

1. ____________________________     1. ___________________________________________

2. ____________________________     2. ___________________________________________

3. ____________________________     3. ___________________________________________

4. ____________________________     4. ___________________________________________

Ex) Write the proof.                                                   Q
P                              R
1 2
Given: QT bisects ∠PTR
QT ⊥ PR
3 4
Prove: ∆PQT ≅ ∆RQT                                              T

Statements (specific)                       Reasons (general)

1. ____________________________     1. ___________________________________________

2. ____________________________     2. ___________________________________________

3. ____________________________     3. ___________________________________________

4. ____________________________     4. ___________________________________________

5. ____________________________     5. ___________________________________________

30 Notes 3.1, Page 4 of 5
L. Morvan, Cypress College
5. AAS Method for proving congruent triangles

AAS:

E                                     G
Ex) Write the proof.

Given: ∠E ≅ ∠G                                                   F
∠EDH ≅ ∠GHD
D                         H
Prove: ∆EDH ≅ ∆GHD

Statements (specific)                             Reasons (general)

1. ____________________________                1. ___________________________________________

2. ____________________________                2. ___________________________________________

3. ____________________________                3. ___________________________________________

(hint: try drawing the triangles separately)

30 Notes 3.1, Page 5 of 5
L. Morvan, Cypress College

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