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Classifying Quadrilaterals and Parallelograms in Geometry

Learn about the properties and relationships of quadrilaterals, including trapezoids, rhombi, rectangles, squares, kites, and parallelograms. Explore how to classify and determine the type of quadrilateral using given information and measurements. Understand the significance of right angles in parallelograms and rectangles.

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Classifying Quadrilaterals and Parallelograms in Geometry

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  1. 6.6 Specialized Quadrilaterals California State Standards for Geometry 7: Prove & use theorems involving parallel lines and properties of quadrilaterals. 8: Solve problems involving perimeter and area. 10: Compute area of polygons 12: Find and use measures of sides and angles of triangles and polygons

  2. quadrilateral relationships Quadrilaterals trapezoids parallelograms rhombi rectangles kites squares

  3. isosceles trapezoid square quadrilateral relationships quadrilateral kite parallelogram trapezoid rhombus rectangle

  4. Example A quadrilateral has at least one pair of opposite sides congruent. What kind of quadrilateral is it? quadrilateral kite parallelogram trapezoid rhombus rectangle isosceles trapezoid square

  5. Examples A quadrilateral has at least two congruent consecutive sides. What kind of quadrilateral is it? quadrilateral sometimes kite parallelogram trapezoid rhombus rectangle isosceles trapezoid square

  6. Example The coordinates of a quadrilateral are (-2, 5), (1, 8), (4, 5), and (1, 2) What kind of quadrilateral is it? Explain. B y The quadrilateral is a square C A D x

  7. Example In quadrilateral RSTV, What kind of quadrilateral is it? Explain quadrilateral parallelogram trapezoid kite rhombus rectangle isosceles trapezoid square

  8. and are not supplementary. Example In quadrilateral RSTV, What kind of quadrilateral is it? Explain S R 88o 113o 113o kite V 46o T

  9. Exactly 1 pair of opp. sides are Both pairs of opp. sides are quadrilateral properties X X X X Both pairs of opp. sides // sorry sorry X Exactly one pair of opp. sides are // sorry sorry sorry sorry sorry X X X X sorry sorry only isosceles sorry sorry sorry sorry sorry X X All sides are congruent sorry sorry sorry sorry

  10. Both pairs of opp. angles are Exactly one pair of opp angles are quadrilateral properties X X X Diagonals are perpendicular sorry sorry sorry X X Diagonals are congruent sorry sorry sorry sorry X X X X Diagonals bisect each other sorry sorry X X X X sorry sorry X sorry sorry sorry sorry sorry X X All angles are congruent sorry sorry sorry sorry

  11. Summary • What characteristics must be considered when classifying a quadrilateral? • Why must a parallelogram with one right angle be a rectangle?

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