html5-img
1 / 13

Given: ZY || WX; WX  ZY Prove:  W   Y

WARM UP - Complete the Proof. Z. Y. Given: ZY || WX; WX  ZY Prove:  W   Y. W. X. 1. WX  ZY, ZY || WX. 1. Given. 2. If lines are parallel, alternate interior angles are congruent. 2. YZX  WXZ. 3. ZX  ZX. 3. Reflexive Property. 4. Δ YZX  Δ WXZ.

tilly
Télécharger la présentation

Given: ZY || WX; WX  ZY Prove:  W   Y

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. WARM UP- Complete the Proof. Z Y Given: ZY || WX; WX  ZY Prove: W Y W X 1. WX  ZY, ZY || WX 1. Given 2. If lines are parallel, alternate interior angles are congruent. 2. YZX  WXZ 3. ZX  ZX 3. Reflexive Property 4. ΔYZX ΔWXZ 4. SAS Postulate 5. W  Y 5. CPCTC

  2. Section 5-1 Properties of Parallelograms

  3. PARALLELOGRAM Definition – A quadrilateral with both pairs of opposite sides parallel.

  4. Theorem 5-1: Opposite sides of a parallelogram are congruent. E F H G EF  GH, FG  EH

  5. F PROOF OF THEOREM 5-1: E 1 2 Given: EFGH Prove: EF  GH, FG  EH 3 4 G H 1. EFGH 1. Given 2. EF || GH, FG || HE 2. Def. of parallelogram 3. If lines are parallel, then alternate interior angles are congruent. 3. 1 4, 2 3 4. FH FH 4. Reflexive Property 5. ΔEFH ΔGHF 5. ASA Postulate 6. EF GH; FG  HE 6. CPCTC

  6. Theorem 5-2: Opposite angles of a parallelogram are congruent. E F H G F  H, E  G

  7. F E PROOF OF THEOREM 5-2: 4 1 Given: EFGH Prove: E  G 2 3 G H 1. EFGH 1. Given 2. EF || HG, EH || FG 2. Def. of parallelogram 3. If lines are parallel, then alternate interior angles are congruent. 3. 4 3, 2 1 4. FH FH 4. Reflexive Property 5. ΔEFH ΔGHF 5. ASA Postulate 6. E  G 6. CPCTC

  8. How can we prove the other opposite angles are congruent using information from the previous proof? F E Given: EFGH, E  G Prove: H  F G H 1. E  G, EFGH 1. Given 2. EF || HG 2. Def. of parallelogram 3. Eand H are supplementary 3. If lines are parallel, same-side interior angles are supplementary. Fand G are supplementary 4. mE + mH = 180 4. Definition of Supp. Angles mF + mG = 180 5. mE + mH = mF + mG 5. Substitution 6. mH = mF, H  F 6. Subtraction

  9. Consecutive angles of a parallelogram are supplementary . E F H G E and H are supplementary E and F are supplementary F and G are supplementary H and G are supplementary

  10. Theorem 5-3: Diagonals of a parallelogram bisect each other. Q R M T S QM  MS, RM  MT

  11. Q PROOF OF THEOREM 5-3: R 1 3 Given: QRST Prove: QS and RT bisect each other M 4 2 S T 1. QRST 1. Given 2. QR || ST 2. Def. of parallelogram 3. If lines are parallel, then alternate interior angles are congruent. 3. 1 2, 3 4 4. QR ST 4. Opposite sides of a parallelogram are congruent. 5. ΔQRM ΔSTM 5. ASA Postulate 6. QM SM; RM  TM 6. CPCTC 7. M is the midpoint of QS and RT 7. Definition of a Midpoint 8. QS and RT bisect each other 8. Def. of Segment Bisector

  12. Review of Properties Name all the properties of a parallelogram. • 2 pairs of opposite sides are parallel • 2 pairs of opposite sides are congruent • 2 pairs of opposite angles are congruent • Diagonals bisect each other • Consecutive angles are supplementary

  13. CLASS WORK Complete 5-1 Class Work worksheet and turn it in when you are finished.

More Related