What is a quadrilateral? -four sided polygon What is a parallelogram? A quadrilateral with - opposite sides parallel - opposite sides congruent - both.

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Presentation transcript:

What is a quadrilateral? -four sided polygon

What is a parallelogram? A quadrilateral with - opposite sides parallel - opposite sides congruent - both pairs of opposite angles congruent - diagonals bisect each other and since it is a quadrilateral: -four sides Is a quadrilateral always a parallelogram? Is a parallelogram always a quadrilateral?

180° midpoint

What is a rectangle? A parallelogram with - four right angles - congruent diagonals and since it is a parallelogram: - opposite sides parallel - opposite sides congruent - both pairs of opposite angles congruent - diagonals bisect each other and since a parallelogram is a quadrilateral: - four sides Is a rectangle always a parallelogram? Is a rectangle always a quadrilateral? Is a parallelogram always a rectangle?

180° diagonals are congruent midpoint

What is a rhombus? A parallelogram with - four congruent sides - perpendicular diagonals - diagonals bisect the angles and since it is a parallelogram: - opposite sides parallel - opposite sides congruent - both pairs of opposite angles congruent - diagonals bisect each other and since a parallelogram is a quadrilateral: - four sides Is a rhombus always a parallelogram? Is a rhombus always a quadrilateral? Could a rhombus be a rectangle?

180° diagonals bisect the angles midpoint

What is a square? A rectangle that is a rhombus: - four right angles - congruent diagonals - four congruent sides - perpendicular diagonals - diagonals bisect the angles and since rectangles and rhombii are parallelograms: - opposite sides parallel - opposite sides congruent - both pairs of opposite angles congruent - diagonals bisect each other and since a parallelogram is a quadrilateral: - four sides

180° diagonals are congruent diagonals bisect the angles midpoint

Is a square always a rectangle? Is a square always a rhombus? Is a rhombus always a square? Is a rectangle always a square? Is a square always a parallelogram? Is a square always a quadrilateral?

What is a kite? A kite is not a parallelogram, so: - opposite sides are not parallel - opposite sides are not congruent - both pairs of opposite angles are not congruent - diagonals do not bisect each other A kite is a quadrilateral with - two pairs of adjacent sides congruent - one pair of opposite angles congruent - one diagonal bisects a pair of opposite angles - the long diagonal bisects the shorter diagonal

polygons quadrilaterals parallelograms rectangles rhombii squares kites

The following points are the vertices of a parallelogram. Find the length of each side, measure of each angle, and length of each diagonal. Also, find the midpoint of each diagonal. Show all work. Oh, and no graph paper, rulers, or protractors allowed!! You can use a calculator, though! - opposite sides parallel - opposite sides congruent - both pairs of opposite angles congruent - diagonals bisect each other P (-5, 3) Q (-1, 5) R (6, 1) S (2, -1)

Start with a sketch. P (-5, 3) Q (-1, 5) R (6, 1) S (2, -1) P Q R S Once you find PQ, what other side do you know? Once you find QR, what other side do you know? What are the diagonals? Where is the midpoint?

The following points will form a quadrilateral. Is the quadrilateral a parallelogram? Provide evidence to support your answer. No graphing allowed!!!!!! Q (10, 13) R (12, 5) S (1, -4) T (-1, 5) Q R S T

Given: ABCD is a square with diagonals AC and BD. E is the point of intersection of the two diagonals. Prove: ΔAEB  ΔDEC A B D C E