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Chapter 4 Proofs

Chapter 4 Proofs. By: Aaron Friedman-Heiman and David Oliver. ASA- Angle Side Angle. Used to prove triangle congruence: if two angles and the included side of two triangles are congruent, then the triangles are congruent. Given: KL and NO are parallel; M bisects KO.

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Chapter 4 Proofs

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  1. Chapter 4 Proofs By: Aaron Friedman-Heiman and David Oliver

  2. ASA- Angle Side Angle Used to prove triangle congruence: if two angles and the included side of two triangles are congruent, then the triangles are congruent. Given: KL and NO are parallel; M bisects KO. Prove: KLM ≡ ONM

  3. Angle Angle Side -Two triangles can be proven to be congruent if two angles and the not included side are congruent. • Given: DE =FG ; DA ll EC; <B and <E are right angles • Prove: ABC = DEF A C B E F G D

  4. Side Angle Side • Given: AB = BC, AD = EC • Prove: ABE = CBD B D E F A C

  5. Hypotenuse-Leg • Given: <1 and <2 are right angles; AB = CB • Prove: ADB = CDB D 1 2 A C B

  6. Side Side Side Theorem B F A D C Given: <1= <2, <3= <4 Prove: AFD= CFD

  7. Base Angle Theorem C A D B proofs Given: AC=BC Prove: <A=<B

  8. A square is a rhombusTheorem A B D C Given: ABCD is a square Prove: ABCD is a rhombus

  9. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram A B E D C Given: BD bisects AC Prove: ABCD is a parallelogram.

  10. If one pair of adjacent sides of a parallelogram are congruent, then the parallelogram is a rhombus. A B D C Given: ABCD is a parallelogram, AB=BC Prove: ABCD is a rhombus.

  11. If the diagonals of a parallelogram bisect the angles of the parallelogram, then the parallelogram is a rhombus. B C E A D Given: ABCD is a parallelogram, BD bisects <ADC and <ABC, AC bisects <BAD and <BCD. Prove: ABCD is a rhombus.

  12. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus: B E A C D Given: ABCD is a parallelogram, BD perpendicular to AC. Prove: ABCD is a rhombus.

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