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Objective: Prove quadrilateral conjectures by using triangle congruence postulates and theorems

4.5 Properties of Quadrilaterals. Objective: Prove quadrilateral conjectures by using triangle congruence postulates and theorems. Warm-Up:. How are the quadrilaterals in each pair alike? How are they different?. Parallelogram vs Square. Rhombus vs Square. Alike:. 4 = sides

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Objective: Prove quadrilateral conjectures by using triangle congruence postulates and theorems

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  1. 4.5 Properties of Quadrilaterals Objective: Prove quadrilateral conjectures by using triangle congruence postulates and theorems Warm-Up: How are the quadrilaterals in each pair alike? How are they different? Parallelogram vs Square Rhombus vs Square Alike: 4 = sides Opp <‘s = Diagonals perp. Alike: Opp sides || & Different: Sq 4 right <‘s Sq 4 sides Different: Sq has 4 right <‘s

  2. Quadrilateral: Any four sided polygon. Trapezoid: A quadrilateral with one and only one pair of parallel sides. Parallelogram: A quadrilateral with two pairs of parallel sides. Rhombus: A quadrilateral with four congruent sides. Rectangle: A quadrilateral with four right angles. Square: A quadrilateral with four congruent sides and four right angles.

  3. PROPERTIES OF SPECIAL QUADRILATERALS: PARALLELOGRAMS: Both pairs of opposite sides are parallel Both pairs of opposite sides are congruent Both pairs of opposite sides angles are congruent Consecutive angles are supplementary Diagonals bisect each other A diagonal creates two congruent triangles (it’s a turn – NOT a flip)

  4. P L M G Theorem: A diagonal of a parallelogram divides the parallelogram into two congruent triangles.

  5. PROPERTIES OF SPECIAL QUADRILATERALS: RECTANGLES: Rectangles have all of the properties of parallelograms plus: Four right angles Congruent Diagonals Perpendicular Sides

  6. PROPERTIES OF SPECIAL QUADRILATERALS: RHOMBUSES: Rhombuses have all of the properties of parallelograms plus: Four congruent sides Perpendicular diagonals Diagonals bisect each other

  7. PROPERTIES OF SPECIAL QUADRILATERALS: SQUARES: Squares have all of the properties of parallelograms, rectangles & rhombuses.

  8. Parallelogram Square Rectangle Rhombus Note: Sum of the interior <‘s of a quadrilateral = _____

  9. Example: Find the indicated measures for the parallelogram WXYZ 5 W X 2.2 Z Y m<WXZ = _____ m<ZXY = _____ m<W = _____ XY = _____ Perimeter of WXYZ= _____ m<WZX = _____

  10. Example: ABDE is a parallelogram & BC BD A B E C D If m<BDC = , find m<EAB. _______ If m<DBC = , m<BCD=6x, find m<EAB ______ If m<DBC = , m<BCD=6x, find m<ABD ______

  11. Example: Find the indicated measure for the parallelogram A m<A = ______ ( B D C

  12. Example: Find the indicated measure for the parallelogram R Q QR = ______ 6x-2 10 S x+4 T

  13. Example: Find the indicated measure for the parallelogram C D ( CD = ______ E F x-7

  14. Example: Find the indicated measure for the parallelogram M N ( m<N = ______ P O

  15. Example: Find the indicated measure for the parallelogram E H ( m<G = ______ F G

  16. Homework: • Practice Worksheet

  17. Parallelograms & Factoring Objective: Identify the missing component of a given parallelogram through the use of factoring. Warm-Up: What is the first number that has the letter “a” in its name?

  18. Example: Find the indicated measure for the parallelogram B A AD = ______ ( C ( D

  19. Example: Find the indicated measure for the parallelogram D E ( m<E = ______ ( G F

  20. Example: Find the indicated measure for the parallelogram R Q ( QR = ______ ( S T

  21. Example: Find the indicated measure for the parallelogram P Q ( m<R = ______ ( S R

  22. Collins Writing: • How could you determine the sum of the interior angles of a quadrilateral?

  23. Homework: • Practice Worksheet

  24. P • Given: L Parallelogram PLGM with diagonal LM 2 • Prove: 1 ∆LGM ∆MPL 4 3 M G • REASONS • STATEMENTS

  25. A B • Given: Parallelogram ABCD with diagonal BD 1 3 • Prove: 4 ∆ABD ∆CDB 2 5 6 D C • REASONS • STATEMENTS

  26. Theorem: Opposite sides of a parallelogram are congruent. • Given: Parallelogram ABCD with diagonal BD • Prove: AB CD & AD CB • REASONS • STATEMENTS

  27. Theorem: Opposite angles of a parallelogram are congruent. • Given: Parallelogram ABCD with diagonals BD & AC • Prove: <BAD <DCB & <ABC <CDA • REASONS • STATEMENTS

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