Geometry Proofs Examples And Answers Pdf - Fill Online, Printable ... - Free Printable

# Geometry Debrief: Proofs Using Triangle Congruence

## #1
STATEMENTS
1. AB ≅ CD, AD ≅ CB (Given)
2. BD ≅ DB (Reflexive Property)
3. △ABD ≅ △CDB (SSS Congruence)

REASONS
1. Given
2. Reflexive Property of Congruence
3. SSS (Side-Side-Side) Congruence Postulate

## #2
STATEMENTS
1. AB ≅ CD, ∠B ≅ ∠D (Given)
2. BD ≅ DB (Reflexive Property)
3. △ABD ≅ △CDB (SAS Congruence)

REASONS
1. Given
2. Reflexive Property of Congruence
3. SAS (Side-Angle-Side) Congruence Postulate

## #3
STATEMENTS
1. AB ≅ CD, ∠B ≅ ∠D (Given)
2. ∠A ≅ ∠C (Alternate Interior Angles Theorem - assuming lines are parallel based on context)
3. △ABD ≅ △CDB (ASA Congruence)

REASONS
1. Given
2. Alternate Interior Angles Theorem (if lines are parallel)
3. ASA (Angle-Side-Angle) Congruence Postulate

## #4
STATEMENTS
1. AB ≅ CD, ∠A ≅ ∠C (Given)
2. BD ≅ DB (Reflexive Property)
3. △ABD ≅ △CDB (SAS Congruence)

REASONS
1. Given
2. Reflexive Property of Congruence
3. SAS (Side-Angle-Side) Congruence Postulate

## #5
STATEMENTS
1. AC ⊥ BC, EC ⊥ DC (Given)
2. ∠ACB ≅ ∠ECD (Right angles are congruent)
3. BC ≅ DC (Given)
4. △ABC ≅ △EDC (SAS Congruence)

REASONS
1. Given
2. Definition of perpendicular lines / All right angles are congruent
3. Given
4. SAS (Side-Angle-Side) Congruence Postulate

## #6
STATEMENTS
1. AB ≅ CD, ∠A ≅ ∠C (Given)
2. ∠B ≅ ∠D (Alternate Interior Angles Theorem - assuming lines are parallel based on context)
3. △ABD ≅ △CDB (AAS Congruence)

REASONS
1. Given
2. Alternate Interior Angles Theorem (if lines are parallel)
3. AAS (Angle-Angle-Side) Congruence Theorem