Week 14 day 1

6

A ceramic tile is in the shape of a 30°-60°-90° triangle. Theside across from the 30° angle is 6.25 cm long. How long is the hypotenuse of the tile?

3.125 cm

6.25 3 cm

12.5 cm

15 cm

A

B

C

D

6.4 Special 6.4 Special ParallelogramsParallelograms

PardekooperPardekooper

What makes a rhombus special?

• All sides are congruentAll sides are congruent

PardekooperPardekooper

What makes a rectangle special?

• Four right anglesFour right angles

PardekooperPardekooper

Put them together and what do you have?

• A squareA square

PardekooperPardekooper

Now, we look at some theoremsNow, we look at some theorems

• Each diagonal of a rhombus Each diagonal of a rhombus bisects two angles of the bisects two angles of the

rhombus.rhombus.

PardekooperPardekooper

Now, we look at some theoremsNow, we look at some theorems

• The diagonals of a rhombus The diagonals of a rhombus are perpendicular.are perpendicular.

PardekooperPardekooper

Now, we look at some theoremsNow, we look at some theorems

• The diagonals of a rectangle The diagonals of a rectangle are congruent.are congruent.

PardekooperPardekooper

Now, we look at some theoremsNow, we look at some theorems• If one diagonal of a If one diagonal of a

parallelogram bisects two parallelogram bisects two angles of the parallelogram, angles of the parallelogram, then the parallelogram is a then the parallelogram is a

rhombus.rhombus.

PardekooperPardekooper

Now, we look at some theoremsNow, we look at some theorems• If the diagonal of a If the diagonal of a

parallelogram are parallelogram are perpendicular, then the perpendicular, then the

parallelogram is a rhombus.parallelogram is a rhombus.

PardekooperPardekooper

Now, we look at some theoremsNow, we look at some theorems• If the diagonal of a If the diagonal of a

parallelogram are congruent, parallelogram are congruent, then the parallelogram is a then the parallelogram is a

rectangle.rectangle.

PardekooperPardekooper

OK, here comes a problem.OK, here comes a problem.ABCD is a rhombus. Solve for X, Y, & Z.ABCD is a rhombus. Solve for X, Y, & Z.

Z = 260

Y = 1280

Y+260+260 = 1800

Y+520 = 1800

-520 -520

X = 1280

A

B

C

D

26 0

Y

X

Z

PardekooperPardekooper

And now the assignment.And now the assignment.

PardekooperPardekooper

AssignmentWorkbook

Page 363 all

PardekooperPardekooper

PardekooperPardekooper

PardekooperPardekooper

PardekooperPardekooper

PardekooperPardekooper