# Key - Chapter 6 Proof Practice.pdf - Chapter 6 Proof...

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Chapter 6 Proof Practice Key 1) Given: A ∠BProve: ACE ~ BCD Statements Reasons 1) A B 1) Given 2) ACE BCD 2) Reflexive 3) ∆ACE ~ ∆BCD3) AA Similarity 2) Given: S ∠VProve: STX ~ VTU Statements Reasons 1) S V 1) Given 2) STX VTU 2) Vertical Angles are congruent 3) ∆STX ~ ∆VTU 3) AA Similarity 3) Given: ??̅̅̅̅||??̅̅̅̅Prove: ABE ~ DCE Statements Reasons 1) ??̅̅̅̅||??̅̅̅̅1) Given 2) BAE CDE 2) Corresponding Angles Congruence Postulate ABE DCE 3) ∆ABE ~ ∆DCE3) AA Similarity ** Can also use vertical angles **
4) Given: 𝑀?̅̅̅̅̅||??̅̅̅̅Prove: ∆MNQ ~ ∆PNOStatements Reasons 1) 𝑀?̅̅̅̅̅||??̅̅̅̅1) Given 2) M P 2) Alternate Interior Angles Congruence Theorem 3) MNQ PNO 3) Vertical Angles are Congruent 4) MNQ ~ ∆PNO 3) AA Similarity ** Can also solve using 2 alternate interior angles ** 5) Given: ∆ABC is a right triangle, ??̅̅̅̅⊥ ??̅̅̅̅Prove: ∆ABC ~ ∆BDC Statements Reasons 1) ∆ABC is a right triangle1) Given 2) ∠ABC is a right angle 2) Definition of right triangle 3) ??̅̅̅̅⊥ ??̅̅̅̅3) Given 4) BDC is a right angle 4) Definition of perpendicular 5) ∠ABC BDC 5) All right angles are congruent 6) C C 6) Reflexive Property 7) ∆ABC ~ ∆ADB7) AA Similarity