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Units 4.3 & 4.4 Proofs & Congruent Triangles

Units 4.3 & 4.4 Proofs & Congruent Triangles. Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.

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Units 4.3 & 4.4 Proofs & Congruent Triangles

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  1. Units 4.3 & 4.4 Proofs & Congruent Triangles

  2. Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. The vertical angles are congruent, so two pairs of angles and a pair of non-included sides are congruent. The triangles are congruent by the AAS Congruence Theorem. EXAMPLE 1 Identify congruent triangles SOLUTION

  3. There is not enough information to prove the triangles are congruent, because no sides are known to be congruent. Two pairs of angles and their included sides are congruent. The triangles are congruent by the ASA Congruence Postulate. EXAMPLE 1 Identify congruent triangles

  4. C F, BC EF A D, GIVEN ABCDEF PROVE EXAMPLE 2 Prove the AAS Congruence Theorem Prove the Angle-Angle-Side Congruence Theorem. Write a proof.

  5. Example #2 – SAS – Postulate Given: N is the midpoint of LW N is the midpoint of SK Prove: N is the midpoint of LWN is the midpoint of SK Given Definition of Midpoint Vertical Angles are congruent SAS Postulate

  6. Example #3 – ASA – Postulate Given: HA || KS Prove: Given HA || KS, Alt. Int. Angles are congruent Vertical Angles are congruent ASA Postulate

  7. Example #4 – Paragraph Proof Given: Prove: is isosceles with vertex bisected by AH. • Sides MA and AT are congruent by the definition of an isosceles triangle. • Angle MAH is congruent to angle TAH by the definition of an angle bisector. • Side AH is congruent to side AH by the reflexive property. • Triangle MAH is congruent to triangle TAH by SAS. • Side MH is congruent to side HT by CPCTC.

  8. Example #5 – Column Proof Given: Prove: has midpoint N Given A line to one of two || lines is to the other line. Perpendicular lines intersect at 4 right angles. Substitution, Def of Congruent Angles Definition of Midpoint SAS CPCTC

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