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# Parallelograms

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### Parallelograms

1. 1. TRAPEZOIDS, KITES, AND OTHER SPECIAL QUADRILATERALS 1
2. 2. TRAPEZOIDS ‐ a quadrilateral with exactly one pair of parallel sides base leg legBase Angles base ISOSCELES TRAPEZOIDS WOULD HAVE ____________ LEGS 2
3. 3. ISOSCELES TRAPEZOIDS1. If a trapezoid is isosceles, then each pair of base angles is congruent. 2. If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. 3. A trapezoid is isosceles if and only if its diagonals are congruent. 3
4. 4. 500 FIND THE OTHER THREE ANGLES Quadrilaterals interior angles add to... 4
5. 5. Show that quadrilateral ADCB is an isosceles trapezoid. Ask yourself, what are the mandatory A characteristics for an isosceles trapezoid?B D C 5
6. 6. Show that quadrilateral ADCB is a trapezoid. C Ask yourself, what are the mandatory characteristics for a trapezoid?B D A 6
7. 7. B C M MIDSEGMENT (only of the legs) N A DMIDSEGMENT THEOREM FOR TRAPEZOIDSMN = (1/2)(AD + BC) 7
8. 8. B 22 C E F A D 50FIND EF 8
9. 9. KITE‐ a quadrilateral that has two pairs of consecutive congruent sides,but opposite sides are not congruent Diagonals are perpendicular One pair of opposite angles are ≅ 9
10. 10. Xthe figure is a kite 12 Y 20 14 W 12 ZFIND WXFIND XY 10
11. 11. Find the other angles if this figure is a kite1320 600 11
12. 12. √29 5Find the RED side 12
13. 13. SPECIAL QUADRILATERALSWHAT WEVE DONE SO FAR... KNOW THIS! QUADRILATERAL KITE PARALLELOGRAM TRAPEZOID RHOMBUS RECTANGLE ISOSCELES TRAPEZOID SQUARE 13
14. 14. QUADRILATERALKITE PARALLELOGRAM TRAPEZOID TRUE / FALSE RHOMBUS RECTANGLE ISOSCELES TRAPEZOID SQUARE1. A square is a parallelogram 5. A rhombus is a rectangle2. A kite is a trapezoid 6. A square is a rhombus3. A rectangle is a square 7. A rhombus is a square4. An isosceles trapezoid is a 8. A quadrilateral is a rectanglequadrilateral 14
15. 15. Quadrilateral ABCD has at least one pair of opposite sides congruent. What kinds of quadrilaterals meet this condition?PARALLELOGRAM RECTANGLE ISOSCELES TRAPEZOID SQUARE RHOMBUS TRAPEZOID 15
16. 16. THE DIAGONALS OF RSTQ ARE PERPENDICULAR.WHAT QUADRILATERALS MEET THIS CONDITION? 16
17. 17. Join the midpoints of the sides of any quadrilateral, what special quadrilateral is formed? 17
18. 18. What type of quadrilateral is this? 0 120 EXPLAIN 1200600 600 18
19. 19. IN QUADRILATERAL RSTV, m<R = 880, m<S = 1130, AND m<V = 1130.WHAT TYPE OF QUADRILATERAL COULD RSTV BE? EXPLAIN 19
20. 20. THE DIAGONALS OF ABCD INTERSECT AT POINT N TO FORM FOUR ≅ ISOSCELES ΔS: ΔANB ≅ ΔCNB ≅ ΔCND ≅ ΔAND. WHAT TYPE OF QUADRILATERAL IS ABCD? EXPLAIN. 20
21. 21. WAYS TO SHOW A FIGURE IS A RHOMBUS:1. All four sides of the quadrilateral arecongruent2. Quadrilateral is a parallelogram and thediagonals are perpendicular3. Quadrilateral is a parallelogram and thateach diagonal bisects a pair of oppositeangles 21
22. 22. SHOW the figure is rhombus... K(2, 5)L(‐2, 3) N(6, 3) M(2, 1) 22
23. 23. PROPERTY Both pairs of opp.  sides are || Exactly 1 pair of opp. sides are || Diagonals are  perpendicular Diagonals are ≅ Diagonals bisect  each other  23
24. 24. HOMEWORK TEST MONDAY BACK WORK DEADLINE THIS FRIDAY (3/13) NB30Pg. 359 ‐ 362 #s 16 ‐ 24 even, 32 ‐ 36 even (graph paper needed) Pg. 367 ‐ 370 #s 8 ‐ 13, 16 ‐ 24 even, 36 (graph paper needed), 51 24