Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick

Transcription

1 Special Quadrilateral Investigation 6.16 and 6.17 U What do we know about convex quadrilaterals so far: four sides four angles the angles sum to 360 we can always draw diagonals that will be in the interior of the quadrilateral D Q What if we start specifying things? We have seven special quadrilaterals that are defined by the specific information we know about them. hey all have special names and the specific information means we can prove additional properties about them. For example, if one (and only one) pair of sides are parallel, do we know more about the sides, angles, diagonals? 1 air of arallel Sides (rapezoid) base leg leg base Co-interior angles between parallel lines are supplementary so the angles on the same leg ( and, and ) are supplementary. We cannot determine anything else about the sides or the diagonals. You will complete the exploration given various pieces of information about the special quadrilaterals. Using the theorems and postulates that we have studied so far, consider if the sides are equal/parallel/perpendicular, if the angles are equal/complimentary/supplementary, and if the diagonals are equal/parallel/perpendicular/bisectors of each other. s you go along, fill in what you have proven in the table on the last page. Day 1 Homework 14: p #2-8 (sketch example or counterexample) 13-18

2 1 air of arallel Sides, other sides are equal (Isosceles rapezoid) I Start by drawing the diagonals to form triangles. Can you prove anything about the lengths of the diagonals? anything about the angles of the trapezoid? do the diagonals bisect each other? do they form any congruent triangles? wo airs of Consecutive Congruent Sides (Kite) K I Start by drawing diagonal K. What can you prove about the sides and angles of the kite? dd the other diagonal. What can you prove about the diagonals (bisect each other, angle bisectors, perpendicular, congruent triangles formed, etc.)?

3 wo airs of arallel Sides (arallelogram) L Start by drawing one diagonal. What can you prove about the sides and angles of the parallelogram? dd the other diagonal. What can you prove about the diagonals (bisect each other, perpendicular, congruent triangles formed, etc.)? For all of the rest of the problems, start with the given information (from the definition) and see what you can prove about the sides (equal? parallel?) and the angles (equal? complementary? supplementary? bisected?). Do the same with the diagonals (equal? bisected? perpendicular?). quiangular (ectangle) C

4 quilateral (hombus) H O M egular (Square) Q S Consider this: If knowing the defined properties gives various other attributes, does the converse also hold true? Does knowing some attributes give you the properties of the definition? If so, how many of them do you need to know?

5 Quadrilateral roperties Checklist Name Defined roperties Side ttributes ngle ttributes Diagonal ttributes rapezoid 1 air of arallel Sides Isosceles rapezoid 1 air of arallel Sides, other sides are equal Kite wo airs of Consecutive Congruent Sides arallelogram wo airs of arallel Sides ectangle quiangular hombus quilateral Square egular