Geometry Warm up:

a= 135°, b=40°, c=105, d=135°

5.5 Properties of Parallelograms

What you already should know about parallelograms:1. They are quadrialterals2. Sum of the interior angles is 360°3. Opposite sides are parallel (2 pair)4. Rhombuses, rectangles, squares are all TYPES of parallelograms

Parallelograms are just as easy as the kites and trapezoids from before!

It is just a matter of knowing the properties of the parallelogram--your mtah skills are already there.

Paralellograms have...1. ≅ opposite angles2. Consecutive supplementry angles3. ≅ opposite sides4. diagonals bisect each other

Try these: They are all parallelograms.

4.

5.6 Properties of Special Parallelograms

What are special parallelograms?That's right-rhombuses, rectangles, squares

Rhombus(diamond)

Rectangle Square

This is all fromlast section

What do we know about these already???1. They are ALL parallelograms SO........

a. opposite <'s and opposite sides are ≅b. opposite sides are parallelc. diagonals bisect each otherd. consecutive angles are supplementarye. are quadrilateralsf. sum of interior angles is 360°

What else about a rhombus?

Well....1. diagonals are perpendicular bisectors of each other (box

in middle like kite)2. diagonals bisect the angles too!3. diagonals divide rhombus into 4 ≅ right triangles

4. 2 lines of reflectional symmetry (2 sets of ≅ triangles)

What else about a rectangle?

They also have...1. diagonals that are congruent2. 2 lines of reflecional symmetry3. diagonals bisect each other4. 2 pairs of isoceles ≅ triangles

5. 4 90° angles

What else about a square?

They also have...1. 4 90° angles2. diagonals that ...

a. bisect each otherb. are perpendicular bisectors of each other (like kite)c. bisect the angles (45°)d. divide square into 4 ≅ isoceles triangles (45°, 45°, 90°)

3. 4 lines of reflection

Try some...