Quadrilateral Lab Day 1

Lab Partner 1______Lab Partner 2______Quadrilateral Lab – Day 1

Part I - Parallelograms

Write the definition of a Parallelogram –

1. a. Using graph 1, plot and label A(-4, 5); B(4, 5); C(2, -1); D(-6, -1). b. Connect all 4 points in order from A->B. c. What shape does it make?

2. How else do you know it’s a parallelogram? Could you prove it? How?

3. What is true about the length of opposite sides? Use facts. (Hint: The distance formula is helpful here.)

4. a. What is the measure of  CBA and  CDA? b. What is the measure of  DAB and  DCB? c. What can you conclude about the measure of the opposite angles?

5. a. What is the measure of  ABC and  BCD? b. What is true about the measure of 2 angles that are adjacent (right next to each other) to each other?

6. Draw a diagonal (a line) from point A to C and another from point B to D.

7. Label the intersection point E and write the coordinates.

8. Find EB, EC and EA, ED (length of each). (Again, the distance formula.)

9. What can you conclude about the diagonals of a parallelogram? Lab Partner 1______Lab Partner 2______

Part II – Rhombus

Write the definition of a Rhombus –

1. If a rhombus is a parallelogram – what else is true? a. About opposite sides?

b. About opposite angles?

c. About their diagonals?

2. Use graph 2 for the following problems. Graph and label the points: A(1,-3); B(-4,- 3); C(-1,1); and D(4,1). Connect the points in order. a. What is the length of each side?

b. What shape does it make?

3. a. Connect B and D (Create a diagonal). What is the m  ABD?

b. m CBD?

c. What is the m  ADB? m  CDB?

d. What does the diagonal do to the 2  ’s?

e. What kind of triangle is ∆ABD?

f. What kind of triangle is ∆BCD?

4. a. Connect A and C. Label the intersection point F.

b. What is the m AFB?

c. What does that mean the m  AFD;  DFC and  CFB are?

d. What can you conclude about the diagonals of a rhombus? Lab Partner 1______Lab Partner 2______

Part III – Rectangles

Write the definition of a rectangle –

1. In graph 3, plot and label the following points: A(-5, 4); B(5, 4); C(5, -2) and D(-5, -2). Connect in order.

2. What shape does it create?

3. Connect A & C and B & D (Create 2 diagonals).

4. What is the length of BD and AC? Hint: You will need to use the distance formula.

5. What can you conclude about the diagonals of a rectangle?

If LMNP is a rectangle, find x & the length of each diagonal. Hint: Draw the rectangle (when in doubt – draw it out!). LN = 3x + 1 and MP = 8x - 4 Lab Partner 1______Lab Partner 2______

Part IV – Square

Write the definition of a square –

1. In graph 4, draw and label with coordinates a square. Make sure it fits the definition of a square.

2. What can you conclude about a square? a. Is it also a parallelogram? How do you know?

b. What can you conclude about it’s diagonals?

c. What can you conclude about it’s sides? Is it a rhombus? Why or Why not?

d. What else can you conclude about the square based on previous rules?

Homework for Day 1 – DRAW OUT every diagram and show ALL work! Lab Partner 1______Lab Partner 2______Quadrilateral Lab – Day 2

Part V - Kites

Write the definition of a Kite –

1. Using graph space 5, plot and label A(-4, 4); B(0, 8); C (4, 4); D (0, -3). Connect all points in order.

2. What shape is it? Could you prove it? How?

3. What is BC? BA? CD? DA?

4. What is the m BCD? What is the m  BAD?

5. What is the m ABC? What is the m  ADC?

6. What can you conclude about the opposite angles of a kite (if anything)?

7. Draw a diagonal from A to C.

8. What kind of triangle is ΔABC? What kind of triangle is ΔACD?

9. Draw a diagonal (or use the y-axis) from B to D.

10. Label the intersection of the 2 diagonals point E. What is the m  BEC? Knowing that, what is the measure of  ’s BEA/CED/DEA?

11. What can you conclude about the diagonals of a kite? Lab Partner 1______Lab Partner 2______

Part VI – Trapezoids and Isosceles Trapezoids

Write the definition of a Trapezoid –

1. In graph 6, plot and label the following points and connect them in order: A(-3,2); B(2,2); C(5,-2); D(-6,-2)

2. What is the length of each side? (Use the distance formula where necessary.)

a. What special type of trapezoid is this and why?

3. Draw diagonals AC and BD. a. What is the length of AC?

b. What is the length of BD?

c. What can you conclude about diagonal lengths in this special type of trapezoid?

Homework for Day 2 – DRAW OUT every diagram and show ALL work! Lab Partner 1______Lab Partner 2______

2. Lab Partner 1______Lab Partner 2______

4. Lab Partner 1______Lab Partner 2______