Two-Column Triangle Proofs

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Presentation transcript:

Two-Column Triangle Proofs Move the “statements” and “reasons” around to correctly complete each proof. Once completed, have Mrs. Honeycutt check over your answers.

Statement Reason  

Statement Reason G is the midpoint of 𝐹𝐻 . Given ∆𝐹𝐺𝐸≅∆𝐻𝐺𝐸   G is the midpoint of 𝐹𝐻 . Given ∆𝐹𝐺𝐸≅∆𝐻𝐺𝐸 Reflexive Property 𝐹𝐺 ≅ 𝐺𝐻 . Definition of midpoint Corresponding parts of congruent triangles are congruent (CPCTC). 𝐸𝐹 ≅ 𝐸𝐻 . <1≅<2 Given 𝐸𝐺 ≅ 𝐸𝐺 . SSS

Statement Reason   Corresponding parts of congruent triangles are congruent (CPCTC). <X and <R are right angles <𝑋𝑀𝑄≅<𝑅𝑀𝑇 ASA 𝑋𝑄 ⊥ 𝑋𝑅 ; 𝑅𝑇 ⊥ 𝑋𝑅 Given ∆𝑋𝑀𝑄≅∆𝑅𝑀𝑇 Vertical angles are congruent 𝑄𝑇 bisects 𝑋𝑅 Definition of bisects 𝑋𝑀 ≅ 𝑀𝑅 Definition of perpendicular. <𝑄≅<𝑇 All right angles are congruent. <𝑋≅<𝑅 Given