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Finding Missing Variables in Parallelograms: Properties and Examples

In this lesson, we explore key properties of special parallelograms, including rhombuses, rectangles, and squares. We will solve for missing variables in parallelograms, specifically examining the sides WX and ZY in parallelogram WXYZ, and using properties of rhombuses and rectangles to find values of x. We will also create a Venn diagram to represent the relationships among the properties of quadrilaterals. Understand the definitions, characteristics, and unique attributes that distinguish these shapes in geometry.

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Finding Missing Variables in Parallelograms: Properties and Examples

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  1. 1. A B 3y 2m - 5 ABCD is //gram Find the missing variables m + 10 2x D C • WXYZ is a parallelogram. If WX = 2x – 11 and ZY = x + 12, find x, WX, and ZY. • MNPQ is a parallelograms. If and , find x.

  2. Special Parallelograms

  3. Special Parallelograms RHOMBUS RECTANGLE SQUARE

  4. RHOMBUS FOUR CONGRUENT SIDES

  5. A quadrilateral is a RHOMBUS if and only if it has four congruent sides

  6. RECTANGLE FOUR RIGHT ANGLES

  7. A quadrilateral is a RECTANGLE if and only if it has four right angles

  8. SQUARE FOUR RIGHT ANGLES AND FOUR CONGRUENT SIDES

  9. RHOMBUS Diagonals Bisect A Pair of Opposite Angles

  10. RHOMBUS 90º Diagonals are Perpendicular

  11. RECTANGLE Diagonals are Congruent

  12. Let's make a Venn Diagram Relating all of the Properties of our quadrilaterals

  13. QUADRILATERALS RHOMBUSES RECTANGLES Squares PARALLELOGRAMS

  14. QUADRILATERALS 1. Polygon 2. 4 sides 1. Opposite Sides are congruent RHOMBUSES 1. Diagonals bisect angles RECTANGLES 2. Diagonals perp Squares 1. 4 rt. angles 3. 4 equal sides 2. Diagonals congruent 2. Opposite Angles are congruent 4. Diagonals Bisect 3. Opposite Sides are parallel 5. Consecutive angles are supplementary PARALLELOGRAMS

  15. PQRS is a rhombus P Q S R

  16. PQRS is a rectangle

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