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Properties of parallelogram...CREated By PIYUSH BHANDARI.......

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Properties of parallelogram...CREated By PIYUSH BHANDARI.......

  1. 1. INTRODUCTIONINTRODUCTION *NAME- PIYUSH BHANDARI *CLASS- 9th *SECTION- ‘B’ *SCHOOL- KENDRIYA VIDHYALAYA *SUBJECT- MATHS P.P.T
  2. 2. Properties ofProperties of ParallelogramsParallelograms
  3. 3. ParallelogramParallelogram A parallelogram is named using all four vertices. You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction. For example, the figure above can be either ABCD or ADCB. Parallelogram 3 AB CD and BC AD Definition: A quadrilateral whose opposite sides are parallel. Symbol: a smaller version of a parallelogram Naming: CB A D
  4. 4. Parallelogram:Parallelogram: A PARALLELOGRAMARALLELOGRAM ( ) is a quadrilateral with two pairs of parallel sides. For example: A B D C
  5. 5. Parallelogram:Parallelogram: A PARALLELOGRAMARALLELOGRAM ( ) is a quadrilateral with two pairs of parallel sides. A B D C is a symbol for a “Parallelogram” ABCD AD BC AB CD
  6. 6. Parallelogram:Parallelogram: Terms to know:  Opposite sides A B D C
  7. 7. Parallelogram:Parallelogram: Terms to know:  Opposite sides AB & DC A B D C
  8. 8. Parallelogram:Parallelogram: Terms to know:  Opposite sides AB & DC ; AD & BC A B D C
  9. 9. Parallelogram:Parallelogram: Terms to know:  Opposite sides AB & DC ; AD & BC Opposite angles A & C AA B D CC
  10. 10. Parallelogram:Parallelogram: A B DD C Terms to know:  Opposite sides AB & DC ; AD & BC Opposite angles A & C ; B & D
  11. 11. Parallelogram:Parallelogram: Terms to know:  Opposite sides AB & DC ; AD & BC Opposite angles A & C ; B & D  Consecutive anglesConsecutive angles A & B; AA B D C
  12. 12. Parallelogram:Parallelogram: Terms to know:  Opposite sides AB & DC ; AD & BC Opposite angles A & C ; B & D  Consecutive anglesConsecutive angles A & B; B & C A BB D CC
  13. 13. Parallelogram:Parallelogram: Terms to know:  Opposite sides AB & DC ; AD & BC Opposite angles A & C ; B & D  Consecutive anglesConsecutive angles C & D; A B DD CC
  14. 14. Parallelogram:Parallelogram: Terms to know:  Opposite sides AB & DC ; AD & BC Opposite angles A & C ; B & D  Consecutive anglesConsecutive angles C & D ; A & D AA B DD C
  15. 15. Parallelogram:Parallelogram: Terms to know:  Opposite sides AB & DC ; AD & BC Opposite angles A & C ; B & D  Consecutive anglesConsecutive angles C & D ; A & D  DiagonalsDiagonals AC & BD A B D C A B D C
  16. 16. When are two trianglesWhen are two triangles congruent?congruent?  If two triangles are congruent, how many pairs of congruent parts can be shown?  Name these. CORRESPONDING SIDES FG ≅ XB GH ≅ BM FH ≅ XM CORRESPONDING ANGLES ∠ F ≅ ∠X ∠ G ≅ ∠B ∠ H ≅ ∠M
  17. 17. Properties of ParallelogramProperties of Parallelogram AB ≅ CD and BC ≅ AD A C and B D∠ ≅ ∠ ∠ ≅ ∠ 180 180 180 180 m A m B and m A m D m B m C and m C m D ∠ + ∠ = ∠ + ∠ = ∠ + ∠ = ∠ + ∠ = o o o o AP ≅ PC 17 1. Both pairs of opposite sides are congruent. 2. Both pairs of opposite angles are congruent. 3. Consecutive angles are supplementary. 4. Diagonals bisect each other but are not congruent BP ≅ PDAC and BDP is the midpoint of . A B CD P
  18. 18. Opposite sides are parallelOpposite sides are parallel A B D C AD BC AB CD Properties ofProperties of ParallelogramsParallelograms
  19. 19. Opposite sides are parallel  Opposite sides are congruentOpposite sides are congruent A B D C Properties ofProperties of ParallelogramsParallelograms
  20. 20. Opposite sides are parallel  Opposite sides are congruent  Opposite angles are congruentOpposite angles are congruent A B D C Properties ofProperties of ParallelogramsParallelograms
  21. 21. AA BB D Opposite sides are parallel  Opposite sides are congruent  Opposite angles are congruent  Consecutive angles are supplementaryConsecutive angles are supplementary C Properties ofProperties of ParallelogramsParallelograms 180BmAm =∠+∠
  22. 22. A B D Opposite sides are parallel  Opposite sides are congruent  Opposite angles are congruent  Consecutive angles are supplementaryConsecutive angles are supplementary C m A m B 180 m B+m C=180 m C+m D=180 m D+m A=180 ∠ + ∠ = ∠ ∠ ∠ ∠ ∠ ∠ Properties ofProperties of ParallelogramsParallelograms
  23. 23. A B D Opposite sides are parallel  Opposite sides are congruent  Opposite angles are congruent  Consecutive angles are supplementary  The Diagonals bisect each otherThe Diagonals bisect each other C EAE EC BE ED ≅ ≅ Properties ofProperties of ParallelogramsParallelograms
  24. 24. A B D Opposite sides are parallelOpposite sides are parallel  Opposite sides are congruentOpposite sides are congruent  Opposite angles are congruentOpposite angles are congruent  Consecutive angles are supplementaryConsecutive angles are supplementary  The Diagonals bisect each otherThe Diagonals bisect each other C E Properties ofProperties of ParallelogramsParallelograms
  25. 25. Properties of SpecialProperties of Special ParallelogramsParallelograms Prove and apply properties of rectangles, rhombuses, and squares. Use properties of rectangles, rhombuses, and squares to solve problems.
  26. 26. A type of special quadrilateral is a rectangle. A rectangle is a quadrilateral with four right angles.
  27. 27. A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides. Like a rectangle, a rhombus is a parallelogram. So you can apply the properties of parallelograms to rhombuses.
  28. 28. A square is a quadrilateral with four right angles and four congruent sides. In the exercises, you will show that a square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three.

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