5.4 Special Quadrilaterals Geometry Ms. Kelly Fall 2010.

5.4 Special Quadrilaterals

Geometry

Ms. Kelly

Fall 2010

Objectives:

Apply the definitions and identify the special properties of a rectangle, a rhombus and a square.

Determine when a parallelogram is a rectangle, rhombus or square.

Properties of Special Parallelograms (draw and label) In this lesson, you will study three special types

of parallelograms: rhombuses, rectangles and squares.

Def: A rhombus is a parallelogramwith four congruent sides

Def: A rectangle is a parallelogram with four right angles.

Def: A square is a parallelogram with four congruent sides and four right angles.

Flow Chart of Parallellograms Each shape has the properties of every group that it

belongs to. For instance, a square is a rectangle, a rhombus and a parallelogram; so it has all of the properties of those shapes.

rhombuses rectangles

squares

Random theorems: ON THE BACK OF YOUR HANDOUT

Thm 5-12: The diagonals of a rectangle are ≅.

Thm 5-13: The diagonals of a rhombus are ⊥.Thm 5-14: Each diagonal of a rhombus bisects two angles of the rhombus.Thm 5-15: The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.Thm 5-16: If an angle of a //gram is a right angle, then the // is a rectangle.Thm 5-17: If 2 consecutive sides of a //gram are ≅, then the //gram is a rhombus.

Handout – quadrilaterals cheat chart Now put the appropriate check marks in the

correct box. Use the theorems and Venn diagram as your guide…..

Whiteboards with partnersTell me what the figure(s) are based on the markings Write square, rectangle or rhombus (you may

have more than one answer)

Let’s practice!!!

Page 186 1-4 5 minutes Work quietly, then we will go over together

1. a. 1, 2, 4, 5, 7, 8, 9, 10, 12

b. 2, 4, 8, 9, 10

c. 2, 5, 9, 12

d. 2, 9

2. 2, 9

3. 4, 8, 10

4. 5, 12

Ex. 3: Using properties of a Rhombus In the diagram at the right,

PQRS is a rhombus. What

is the value of y?

All four sides of a rhombus are , so RS = PS.≅5y – 6 = 2y + 3 Equate lengths of sides.≅ 5y = 2y + 9 Add 6 to each side.

3y = 9 Subtract 2y from each side.

y = 3 Divide each side by 3.

5y - 6

2y + 3

P

S

Q

R

Classwork Wrksheet collected and graded Homework page 187 11-19

Closure (on little piece of paper)

5.4 Day 2Warm up Answer True or False for the following statements:

1. A square is a rhombus.

2. Diagonals of a rhombus bisect each other.

3. Diagonals of a rectangle bisect the angles.

4. The diagonals of a square are perpendicular to each other.

5. Opposite angles of a parallelogram are congruent.

6. All angles of a parallelogram are congruent.

7. A square has four congruent sides.

8. A rhombus has four congruent sides.

9. A rectangle is a square.

10. A rectangle has only one pair of 90 angles.

Homework Answers – I am going to call on you!11. 25, 65, 65, 90

12. 4

13. 10

14. 18, 72, 72

15. 13.5

16. 2

17. 32, 58, 58

18. 9

19. .5

Activity

Fold paper in half hamburger style and label the following:

Activity

With a pencil, draw a large shape of what’s labeled

You will now need to pick 4 colors. Designate the following: parallel lines, angles, sides diagonals

http://www.algebra.com/algebra/homework/Polygons/Geometry-Special-Quadrilaterals.lesson

Who am I? Write you answers down. You may have more than one answer. I have four right angles. My diagonals are congruent. My diagonals bisect each other. My diagonals bisect two angles. My diagonals are perpendicular. I have 4 congruent sides. My opposite angles are congruent. I have 4 right angles and opposite sides are

congruent.

Notecard activity Use last night’s homework as a guide On a notecard create the problem – one on

the front and one on the back. Keep the answers separate from the

problem. Assignment on the whiteboard. Do your own, but help each other! Put your name on both sides at the top right. I will collect and correct when done.

Homework

Create 10 True/False problems with a key