G.7 Similar Triangles (Proofs)

• 3 Definition of Congruence

  4 Division Property of Equality

  5 SSS Similarity

• 3 Symmetric Property of Equality

  4 Division Property of Equality

  5 SAS Similarity

• 3 Definition of Congruence

  4 Transitive Property of Equality

  5 AA Similarity

• 3 Definition of Congruence

  4 Division Property of Equality

  5 SAS Similarity

• 3 ∠ABF ≅ ∠DCF

  4 SAS Similarity

• 3 ∠A ≅ ∠D

  4 AA Similarity

• 3 ∠AFB ≅ ∠DFC

  4 AA Similarity

• 3 ∠ABF ≅ ∠DCF

  4 SAS SImilarity

• 3 ∠DFC ≅ ∠BFA; ∠DAB ≅ ∠BCD

  4 Angle-Angle (AA) Postulate

• 3 ∠CBA ≅ ∠ADC; ∠BAD ≅ ∠DCB

  4 Angle-Angle (AA) Postulate

• 3 ∠CDA ≅ ∠BAD; ∠CBA ≅ ∠BCD

  4 Angle-Angle (AA) Postulate

• 3 ∠DFC ≅ ∠BFA; ∠DAB ≅ ∠BCD

  4 Side-Angle-Side (SAS) Postulate

• 2 ∠ACB ≅ ∠DCG Vertical angles are congruent

  3 ∠B ≅ ∠DCG Alternate exterior angles of parallel lines are congruent

• 2 ∠A ≅ ∠DCG Alternate interior angles of parallel lines are congruent

  3 m∠G + m∠ACB = 180 Same side interior angles of parallel lines are supplementary

• 2 ∠B ≅ ∠DCG Alternate interior angles of parallel lines are congruent

  3 ∠G ≅ ∠ACB Corresponding angles of parallel lines are congruent

• 2 ∠A ≅ ∠DCG Corresponding angles of parallel lines are congruent

  3 ∠G ≅ ∠ACB Corresponding angles of parallel lines are congruent

• 1 Given

  2 Given

  3 All right ∠s are ≅

  4 AA Similarity

  5 The ratio of the corresponding sides of similar Δs are in proportion

• 1 Given

  2 Given

  3 Vertical ∠s are ≅

  4 AA Similarity

  5 The ratio of the corresponding sides of similar Δs are in proportion

• 1 Given

  2 Given

  3 All right ∠s are ≅

  4 SAS Similarity

  5 The ratio of the corresponding sides of similar Δs are in proportion

• 1 Given

  2 Given

  3 Vertical ∠s are ≅

  4 SAS Similarity

  5 The ratio of the corresponding sides of similar Δs are in proportion

• 2 Vertical ∠s are ≅.

  3 ∠B ≅ ∠CDE

  4 SAS

• 2 Corresponding ∠s are ≅.

  3 ∠AEB ≅ ∠DEC

  4 AA

• 2 Corresponding ∠s are ≅.

  3 ∠B ≅ ∠CDE

  4 AA

• 2 Vertical ∠s are ≅.

  3 ∠AEB ≅ ∠DEC

  4 SAS

• 1 Given

  2 Addition Postulate

  3 Substitution Property

  4 Transitive Property

  5 Reflexive Property

  6 SAS

• 1 Given

  2 Addition Postulate

  3 Substitution Property

  4 Symmetric Property

  5 Reflexive Property

  6 SAS

• 1 Given

  2 Addition Postulate

  3 Substitution Property

  4 Transitive Property

  5 Symmetric Property

  6 SAS

• 1 Given

  2 Addition Postulate

  3 Substitution Property

  4 Transitive Property

  5 Symmetric Property

  6 AA

• 1 AD // BC

  2 ∠BEA ≅ ∠DEC

  3 ∠BEC ≅ ∠AED

  4 ΔAED ∼ ΔBEC

• 1 AD // BC

  2 ∠EDA ≅ ∠ECB

  3 ∠BEC ≅ ∠AED

  4 ΔAED ∼ ΔBEC

• 1 AD // BC

  2 ∠BEC ≅ ∠AED

  3 ∠EDA ≅ ∠ECB

  4 ΔAED ∼ ΔBEC

• 1 AD // BC

  2 ∠BEA ≅ ∠DEC

  3 ∠EDA ≅ ∠ECB

  4 ΔAED ∼ ΔBEC

• 1 Given

  2 ∠PAQ ≅ ∠CAQ

  3 Equality Property

  4 ΔQAP ∼ ΔBAC

• 1 Given

  2 ∠APQ ≅ ∠ACB

  3 Reflexive Property

  4 ΔQAP ∼ ΔBAC

• 1 Given

  2 ∠APQ ≅ ∠ABC

  3 Equality Property

  4 ΔQAP ∼ ΔBAC

• 1 Given

  2 ∠PAQ ≅ ∠CAQ

  3 Reflexive Property

  4 ΔQAP ∼ ΔBAC

• 1 Given

  2 ∠N ≅ ∠Q

  3 AA

• 1 Given

  2 ∠N ≅ ∠Q

  3 SSS

• 1 Given

  2 ∠N ≅ ∠Q

  3 SAS

• 1 Given

  2 ∠N ≅ ∠R

  3 AA