Geometry
Notes Section 6.1
Name ________________________
True or False. Answer the questions to the best of your current knowledge of four-sided polygons.
1. Every rectangle is a parallelogram. __________
2. If it is a quadrilateral, then it is a rectangle. __________
3. All rhombuses are squares. __________
4. Every rhombus is a parallelogram. __________
5. All squares are rectangles. _____________
6. If a quadrilateral is a parallelogram, then it is a rectangle. ________
7. Some parallelograms are rectangles. ____________
8. All parallelograms are quadrilaterals. __________
9. Every rectangle is a square. __________
10. Every rhombus is a kite and a rectangle. __________
Characteristics of Quadrilaterals.
Go to page 306 and list the characteristics for the quadrilaterals listed below.
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Quadrilateral: A Polygon with 4 sides and 4 vertices (corners)

Parallelogram: ______________________________________________________________________
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Rhombus: __________________________________________________________________________

Rectangle: _________________________________________________________________________

Square: ___________________________________________________________________________
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Kite: ______________________________________________________________________________
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Trapezoid: __________________________________________________________________________
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Isosceles Trapezoid: __________________________________________________________________
After listing the characteristics, would you change any of the answers from the True or False section? ________
If yes, which questions?
Copy the quadrilateral chart from page 307. (You do not have to list the characteristics again.)
Rule for the Chart: If you move up the chart, the answer will be true. If you move down the chart, the answer will be false.
Revisit the True or False Questions with the rule stated above. If the answer is ‘false’ give a counterexample!
1. Every rectangle is a parallelogram. __________
2. If it is a quadrilateral, then it is a rectangle. __________
3. All rhombuses are squares. __________
4. Every rhombus is a parallelogram. __________
5. All squares are rectangles. _____________
6. If a quadrilateral is a parallelogram, then it is a rectangle. ________
7. Some parallelograms are rectangles. ____________
8. All parallelograms are quadrilaterals. __________
9. Every rectangle is a square. __________
10. Every rhombus is a kite and a rectangle. __________
Stop Here. Stop Here. Stop Here. Stop Here. Stop Here. Stop Here. Stop Here. Stop Here. Stop Here. Stop Here.
Notes.
To prove congruent sides (length):
To prove parallel or perpendicular sides (slope):
Distance formula _________________________________________
Slope = _______________
You will be given the precise name of the quadrilateral. Graph and prove it by using the definitions given before.
1. Rhombus. What must you prove? _________________________________ and _______________________________________
A(3, 5), B(7, 6), C(6, 2), D(2, 1)
2. Kite. What must you prove? _________________________________________________________________________________
W(-1, 1), X(0, 2), Y(1, 1), Z(0, -2)
3. Trapezoid. What must you prove? __________________________________________________________________________
J(2, 1), K(5, 4), L(7, 2), M(2, -3)
Find the values of the variables. Then find the length of the sides.