1. Properties of Other Quadrilaterals Students will be able to… Identify and use the properties of rectangles, squares, rhombuses, kites, and trapezoids

2. The following quadrilaterals have perpendicular diagonals: Rhombus Square Kite

3. The following quadrilaterals have opposite angles that are bisected: Rhombus Square

4. Example: Find the measures of the numbered angles in the rhombus. 1 2 3 4 12°

5. The figure below is a rhombus. Find TQ, TP, and SQ.

6. The following quadrilaterals have congruent diagonals Rectangle Square Isosceles Trapezoid

7. EXAMPLE BD=5y-7 and AC = y + 5. Find the value of y and the length of BE. E

8. EXAMPLE: If BD= 2x+10 and AC=x+15, find x and the length of the diagonals.

9. TRAPEZOID LEG BASE ANGLES The 2 parallel sides are the bases The 2 non-parallel sides are the legs A B C D Name the following: Bases: Legs: 2 Pairs of Base Angles:

10. The following quadrilaterals have exactly one pair of opposite parallel sides Trapezoid Isosceles Trapezoid The following quadrilaterals have exactly one pair of opposite congruent sides: Isosceles Trapezoid

11. Theorem: The base angles of an isosceles trapezoid are congruent A B C D Example- Find x given the following angle measures:

12. The following quadrilaterals have exactly one pair of opposite congruent angles Kite

13. Example: Find the measures of the numbered angles. 46° 3 2 1

14. 44°112° 1 2 FIND THE MEASURE OF THE MISSING ANGLES., assign x to represent each measure. So equation will be: 44+112+x+x = 360 How many degrees in a quadrilateral? What do we know about the relationship between angles 1 and 2?

15. 2 angles that share a leg in a trapezoid are supplementary because they are same-side interior angles.

16. The following is an isosceles trapezoid. The measure of angle A= 110. Find the measures of the other 3 angles.

17. Midsegment (Median) of a Trapezoid Joins the midpoints of the nonparallel sides Is parallel to the bases Its length is ½ the sum of the bases MN || BC MN || AD MN = ½(BC+AD)

18. 4 3 86 ° 108° Find the following: EF:

19. Find x: 8 12 x