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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.

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Presentation on theme: "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."— Presentation transcript:

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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 StatementsReasons KL and NO are parallel; M bisects KO. KML OMN MKL MON KM MO KLM ONM Given Vertical Angles Alt. Interior Definition of bisect ASA

3 Angle Angle Side -Two triangles can be proven to be congruent if two angles and the not included side are congruent. StatementsReasons DE=FG; DA ll EC;

4 Side Angle Side StatementsReasons AB = BC; AD = EC Given AB = CBSegment Addition

5 Hypotenuse-Leg StatementsReasons <1 and <2 are right angles; AB = CB Given <1 = 90° <2 = 90° Definition right angle <1 = <2Transitive Property BD = BDReflexive Property ADB = ___CDB HL Given: <1 and <2 are right angles; AB = CB Prove: ADB = CDB A CB D 1 2

6 Side Side Side Theorem Given: <1= <2, <3= <4 Prove: AFD= CFD StatementsReasons <1= <2, <3= <4Given BF=BFReflexive ABF= CBFASA AB=BCCPCTC AF=CFCPCTC ABC is isosceles Def of isosceles BD – angle bisector Def- angle bisector BD- perpendicular bisector Angle bisector of the vertex angle of an isos. triangle is a perpendicular bisector of the base AD=CD Def of perpendicular bisector FD=FDreflexive AFD= CFDSSS A D C B F

7 Base Angle Theorem Given: AC=BC Prove:

8 A square is a rhombus Theorem StatementsReasons ABCD is a squareGiven AB=BC=CD=DADefinition of a square ABCD is a rhombus Definition of a Rhombus Given: ABCD is a square Prove: ABCD is a rhombus A B D C

9 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram StatementsReasons BD bisects ACGiven BE=ED, AE=ECDefinition of a bisector

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

11 If the diagonals of a parallelogram bisect the angles of the parallelogram, then the parallelogram is a rhombus. StatementsReasons ABCD is a parallelogram, BD bisects

12 If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus: StatementsReasons ABCD is a parallelogram, BD perpendicular to AC. Given BE=BEreflexive AE=ECDiagonals of a parallelogram bisect


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