4.4A/4.5A Congruent Triangle Proofs
Geometric Proof - A step-by-step explanation that uses definitions, axioms, postulates, and previously
proved theorems to draw a conclusion about a geometric statement. There are two major types of proofs:
direct proofs and indirect proofs.
Direct Proof - A proof in which the conclusion is drawn directly from previous conclusions, starting
with the first statement.
Indirect Proof - A proof in which a statement is shown to be true because the assumption that its
negation is true leads to a contradiction.
Auxiliary Lines - Lines that are created to help prove a statement.
flowchart- a concept map that shows a step-by-step process. Boxes represent the steps, and arrows
connect the boxes to order the process.
flowchart proof- A kind of proof in which a logical argument is presented in the form of a flowchart
.
Paragraph Proof - A kind of proof in which the steps are written out in complete sentences, in
paragraph form.
Two-column Proof – A kind of proof in which the statements (conclusions) are listed in one column, and
the reasons for each statement's truth are listed in another column.
***Note***
When writing any geometric proof, first mark pictures with all given information.
Geometry Lesson 4.4A/4.5A: Congruent Triangle Proofs
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Examples: Write a two- column proof for each.
1.
̅̅̅̅ ≅ DE
̅̅̅̅ ,
Given: AB
E
B
B  E,
̅̅̅̅
̅̅̅̅
BC ≅ EF
A
C
F
D
Prove: ∆ABC  ∆DEF
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
Geometry Lesson 4.4A/4.5A: Congruent Triangle Proofs
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2.
Given: E is the midpoint of ̅̅̅̅
BD ,
C
̅̅̅̅
̅̅
AE ≅ ̅̅
EC
B
Prove: ∆AEB  ∆CED
E
D
A
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
Geometry Lesson 4.4A/4.5A: Congruent Triangle Proofs
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Given: B is the midpoint of ̅̅̅̅
AE ,
3.
D
C
A  E,
CBA  DBE,
A
B
Prove: ∆ABC  ∆EBD
E
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
Geometry Lesson 4.4A/4.5A: Congruent Triangle Proofs
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4.
B
Given: ̅̅̅̅
AB ≅ ̅̅̅̅
CD ,
C
̅̅̅̅ ≅ CB
̅̅̅̅,
AD
Prove: ∆ABD  ∆CDB
A
D
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
Given: A  D,
5.
B
D
BCA  BCD
Prove: ∆ABC  ∆DBC
C
A
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
Geometry Lesson 4.4A/4.5A: Congruent Triangle Proofs
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6.
Given: ̅̅̅̅
CB ⊥ ̅̅̅̅
DA
C
̅̅̅̅ ≅ AC
̅̅̅̅
DC
Prove: ∆DBC  ∆ABC
D
B
A
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
Homework: Complete Worksheet: Triangle Proofs
Geometry Lesson 4.4A/4.5A: Congruent Triangle Proofs
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