 # Review & Trapezoids. Properties of a Parallelogram A BC D 1. Opposite sides are parallel. 2 Opposite sides are congruent. 3. Opposite angles are congruent.

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Review & Trapezoids

Properties of a Parallelogram A BC D 1. Opposite sides are parallel. 2 Opposite sides are congruent. 3. Opposite angles are congruent. 5. Diagonals bisect each other 4. Consecutive angles are supplementary YES, we’re going to review again, & again, & again…

Properties of a Rhombus ABCD 1. Opposite sides are parallel. 2 Opposite sides are congruent. 3. Opposite angles are congruent. 5. Diagonals bisect each other 4. Consecutive angles are supplementary 6. 4 congruent sides 7. Diagonals of a rhombus bisect the angles 8. Diagonals of a rhombus are perpendicular (bisectors)

Properties of a Rectangle 1. Opposite sides are parallel. 2 Opposite sides are congruent. 3. Opposite angles are congruent. 5. Diagonals bisect each other 4. Consecutive angles are supplementary 6. 4 congruent sides 7. Diagonals of a rhombus bisect the angles 8. Diagonals of a rhombus are perpendicular (bisectors) 9. 4 right angles 10. Diagonals are congruent

Properties of a Square 1. Opposite sides are parallel. 2 Opposite sides are congruent. 3. Opposite angles are congruent. 5. Diagonals bisect each other 4. Consecutive angles are supplementary 6. 4 congruent sides 7. Diagonals of a rhombus bisect the angles 8. Diagonals of a rhombus are perpendicular (bisectors) 9. 4 right angles 10. Diagonals are congruent It has it ALL!!!

Practice with squares A B CD BX= AX = DB = AC = 8.5 17 AB= BC= 12 X DX = 8.5 m  AXB= m  XAB=90  45 

And now…Properties of Trapezoids

Definition of a Trapezoid- exactly one pair of parallel sides OR A quadrilateral with:

Definition of a Trapezoid- Parallel sides are called BASES base leg Other nonparallel sides are called LEGS

Definition of an ISOSCELES Trapezoid- A trapezoid with Congruent legs base leg AND Congruent base angles

Name the following for trapezoid RSTW R S WT THE BASES: THE LEGS: ONE PAIR OF BASE ANGLES  R &  S ; or  T &  W

Median of a Trapezoid A M D B N C 6 14 10 The median of any trapezoid is parallel to the bases The median is equal to half the SUM of the base lengths A median (MN) is a segment connecting the midpoints of the legs MN = 10 > > (sum of bases) (half of sum)

Examples – find the length of the median 5 19 11-x 21+x 10 5 3 3 4 4 12 16 7.5

EF= m  1= m  2= m  3= m  4= m  5= 2 78  3 130  4 5 1 15 9 A B C D E F 12 50  102  78  50  130  Isosceles trapezoid? Corr  s  Base  s  Same Side interior - supplementary Corr  s  Same Side interior - supplementary

EF= m  1= m  2= m  3= m  4= m  5= 2 51  3 4 4 5 1 11 6 E F J K L M 16 51  129  51  129  51  Isosceles trapezoid?

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