Given: WXYZ is a parallelogram Prove: Δ YZX Δ WXZ

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Statements Reasons Given: WXYZ is a parallelogram Prove: ΔYZX ΔWXZ W X Y Z 1) Complete the Proof. 2. WX ZY, WZ YX 1. WXYX is a 3. ZX ZX 4. ΔYZX ΔWXZ 1. Given 3. Reflexive Property 2. Opposite sides of a parallelogram are congruent. 4. SSS Postulate

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WARM UP. 1) Complete the Proof. Z. Y. Given: WXYZ is a parallelogram Prove: Δ YZX  Δ WXZ. W. X. 1. WXYX is a. 1. Given. 2. Opposite sides of a parallelogram are congruent. 2. WX  ZY, WZ  YX. 3. ZX  ZX. 3. Reflexive Property. 4. Δ YZX  Δ WXZ. - PowerPoint PPT Presentation

Transcript of Given: WXYZ is a parallelogram Prove: Δ YZX Δ WXZ

  • Given: WXYZ is a parallelogram

    Prove: YZX WXZWXYZ1) Complete the Proof.2. WX ZY, WZ YX 1. WXYX is a 3. ZX ZX4. YZX WXZ1. Given 3. Reflexive Property2. Opposite sides of a parallelogram are congruent.4. SSS Postulate

    StatementsReasons

  • Given: BCDE is a parallelogram AE CD

    Prove: EAB EBABCDE2) Complete the Proof.2. EB DC1. BCDE is a 3. AE CD4. EB AE1. Given 3. Given 2. Opposite sides of a parallelogram are congruent.4. SubstitutionA5. EAB EBA5. If two sides of a triangle are , then the angles opposite those sides are .

    StatementsReasons

  • Pg.168 Def. of Parallelogram If lines are ||, alternate interior angles are congruent. Opposite angles of a parallelogram are congruent. Opposite sides of a parallelogram are congruent. Diagonals of a parallelogram bisect each other. Diagonals of a parallelogram bisect each other.Pg.169a = 8, b = 10, x = 118, y = 62a = 8, b = 15, x = 80, y = 70a = 5, b = 3, x = 120, y = 22a = 9, b = 11, x = 33, y = 27a = 8, b = 8, x = 56, y = 68 a = 10, b = 4, x = 90, y = 45

  • Pg.169 Perimeter = 60 ST = 14, SP = 13

    Pg.170 x = 3, y = 5 x = 7, y = 18 x = 13, y = 5

  • 1) Name all the properties of a parallelogram.2 pairs of opposite sides are parallel2 pairs of opposite sides are congruent2 pairs of opposite angles are congruentConsecutive angles are supplementaryDiagonals bisect each other

  • DAC _____

    AB = _____

    mBCD = _____

    CM = _____ AD || _____

    DA = _____

    BAC _____

    BM = _____Given the below parallelogram, complete the statements.BCA mDAB DCA CDAMBCBCDM

  • Theorem 5-4: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  • PROOF OF THEOREM 5-4:Given: EF GH, FG EH

    Prove: EFGH is a 6. Def. of parallelogram3. EFH GHF3. SSS Postulate4. CPCTC4. 1 4, 2 32. Reflexive Property5. If alternate interior angles are congruent, then lines are parallel.1. Given

  • Theorem 5-5: If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.

  • PROOF OF THEOREM 5-5:Given: EF GH, EF || GH

    Prove: EFGH is a 6. If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram.4. EFH GHF4. SAS Postulate5. CPCTC2. 1 43. Reflexive Property2. If lines are parallel, alternate interior angles are congruent.1. Given

  • Theorem 5-6: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  • PROOF OF THEOREM 5-6:DCBAxyyxGiven: mA = mC = y;mB = mD = x

    Prove: ABCD is a 6. Def. of parallelogram3. x + y = 180 3. Division Property4. Definition of supp. anglesA and D are supp.2. The sum of the interior angles of a quadrilateral is 360.5. If same-side interior angles are supplementary, then lines are parallel.2. 2x + 2y = 360 1. mA = mC = y;mB = mD = x 1. GivenA and B are supp.

  • Theorem 5-7: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

  • Based on the markings on each figure, A. Decide if each figure is a parallelogram (YES or NO). B. If yes, justify your answer. State the theorem that is supported by the figure. If no, identify which theorem is not justified or is not met by the diagram.

  • EXAMPLE 1:EXAMPLE 2:NOYESOpposite sides are not congruent.Both pairs of opposite sides are parallel.

  • EXAMPLE 3:EXAMPLE 4:YESYESDiagonals bisect each other.Both pairs of opposite angles are congruent.

  • EXAMPLE 5:EXAMPLE 6:NOYESPair of congruent/parallel sides is not the same pair of sides.One pair of sides is both congruent and parallel.