The Quadrilateral Family Tree

1. The Quadrilateral Family Tree Created by Tony McCullers, Edited by Mindy Griffis M4G1. Students will define and identify the characteristics of geometric through examination and construction. c. Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi). d. Compare and contrast the relationships among quadrilaterals. QCC - Euclidean Geometry (10th grade) #19 States and applies properties of triangles and quadrilaterals such as parallelograms, rectangles, rhombi, squares, and trapezoids. # 21 Uses properties of quadrilaterals to establish and test relationships involving diagonals, angles, and lines of symmetry.

2. Quadrilateral Def: 4 sides, 4 vertices A + B + C + D = 360° • Parallelogram • Def: opposite sides are parallel • 1. The opposite sides are congruent. • The opposite angles are congruent. • The consecutive angles are supplementary. • The diagonals bisect each other.

3. Rectangle • Have four right angles. • The diagonals are congruent.

4. Rhombus • All 4 sides are congruent. • The diagonals are perpendicular. • The diagonals bisect the angles.

5. Rhombi Rectangles Squares A square has all of the properties of Rectangles and Rhombi!

6. Quadrilateral Parallelogram Rhombus Rectangle The Quadrilateral Family Tree To be discussed on a later date… Square

7. Examples Decide whether the statement is true ALWAYS, SOMETIMES, or NEVER . 1. A rectangle is a square • SOMETIMES 2. A square is a rhombus. • ALWAYS • A rectangle is a parallelogram • ALWAYS

8. Examples 4. QRST is a square. What else do you know about QRST? 5. EFGH is a rectangle. K is the midpoint of FH. FH = 10. (Draw it!) • Find KF. • Find EG. • Find EK. GO TO PAGE 351.

9. Page 351 • Equilateral Quadrilateral Rhombus or Square • All sides are congruent Rhombus or Square 8. All angles are congruent Square, Rectangle 9. Diagonals are congruent Square, Rectangle 10. Opposite angles are congruent Parallelogram, Rectangle, Rhombus, Square

10. HOMEWORK: P. 351 (#16 – 38 even) Only 12 problems.

11. Quadrilateral Parallelogram Rhombus Rectangle The Quadrilateral Family Tree To be discussed today! Square

12. Consecutive Interior Angles Legs Base Angles Base Angles Consecutive Interior Angles D Trapezoids A B C • Def: only ONE PAIR of parallel sides • The parallel sides are called bases. • The other two sides are the legs. • Consecutive interior angles are supplementary.

13. Example T S 145° 68° U R

14. Midsegment of a Trapezoid Def: a segment that joins the midpoints of the Trapezoid’s legs. Length of Midsegment = ½ (Base+Base)

15. Example 22cm 54cm

16. Isosceles Trapezoids • The legs are congruent. • Each pair of base angles are congruent. • Diagonals are congruent!

17. Example CDEF is an isosceles trapezoid with CE=10 and E=95°. Find DF. Find the measure of angles C, D, and F. C D F E

18. Go to Page 359 Homework: p.359 (10 - 24 even)

19. Quadrilaterals Trapezoids Parallelograms Rhombi Rectangles The Quadrilateral Family Tree Let’s finish it up! Isosceles Trapezoids Squares

20. A D B Kites C • NO PAIRS OF PARALLEL SIDES! • Def: two pairs of consecutive sides that are congruent, but opposite sides are not congruent. • Exactly one pair of opposite angles are congruent. • The diagonals are perpendicular.

21. Example 126° 80° 100°

22. 3 4 4 7 Example K Given: HIJK is a kite. Find the measure of each side. KH = 5 KJ = 5 HI = 8.1 JI = 8.1 J H I

23. Quadrilaterals Trapezoids Parallelograms Kites Rhombi Rectangles The Quadrilateral Family Tree Isosceles Trapezoids Squares

24. Go to page 360 • Do # 28 and 32 #28 Find AB=AD = ? And CB=CD=? #32 Find mH and m G.

25. Parallelograms Trapezoids Rectangles Isosceles Trapezoids Rhombi Quadrilaterals Squares Kites