Fourth Six Weeks’ Test Review

For the purposes of this presentation...

Assume that triangles which appear to be right triangles are.

Assume that lines that appear to be perpendicular are.

4

25x =10

The The Pythagorean Pythagorean TheoremTheorem

6

8

x =10

12

18

x 21.63

20

16

x=12

1515

24

x

1515

24

X= 9

1212

Special Right Special Right TrianglesTriangles

45o

x

12 2

=12

x

10

1010 2

30o

20x

y

10

10 3

10 10

10

x5 3

Find the Geometric mean between 4 and 25.

=10

NM=9, MK=4, Find JM.

=6

What equation can be formed?

g

t

m

2 2 2g t m

What kind of triangle has sides 41, 40 and 9?

Right

What kind of triangle has sides of 8, 12 and 18? Obtuse

Find the leg of the right triangle:

15

17

x =8

Find x

8

8

x 8 2

An equilateral triangle has a side of 12. What is its altitude?

6 3

Which ratio is: The opposite leg over the hypotenuse?

The Sine Ratio

Which ratio is: The adjacent leg over the hypotenuse?

The Cosine Ratio

What makes up the tangent ratio?

The opposite leg over the adjacent leg

Set Up the Trig Set Up the Trig ratio to find xratio to find x

20

28o

x

cos 2820

x

17.66

9x

50o

9sin 50

x

11.75

x21

32

x21

32

Tan x = 21/32

x21

32

1 21tan

32x

33.27

What’s true about an interior and exterior angle of a polygon?

Supplementary

For polygons to “fit” around a vertex, the sum of their interior angles must be 360

A regular n-gon has lines of symmetry and rotational of360/n degrees

n

Find the sum of the interior angles of a decagon:

1440

Find the measure of 1 interior angle of a regular 18-gon

160

Find the sum of the exterior angles of a 55-gon

360

Find the measure of one exterior angle of a regular 24-gon

15

The sum of the interior angles of what polygon is 4500? 27-gon

The measure of 1 interior angle of what regular polygon is 170?

36-gon

The measure of 1 exterior angle of what regular polygon is 8?

45-gon

A regular octagon has 8 lines of symmetry and what degree of rotation? 45

The sum of its interior angles is 4 times the sum of its exterior angles. decagon

?

What regular polygon is missing

Another hexagon

What regular polygon is missing

?

Another Octagon

What’s the symmetry of a regular decagon?

10 lines, 36 degr. rotational

Find x (Given a regular octagon)

x

X = 90 degrees

What 3 regular polygons will tessellate the plane?

Equilateral triangles

Regular Hexagons

Squares

Which special quadrilateral has the symmetry described...

- No lines

- 180o rotational

Answer: Parallelogram

Complete the Complete the Theorem….Theorem….

The diagonals of a parallelogram_________.

…bisect each other.

Opposite sides of a parallelogram are__________.

…congruent.(They are also parallel, but that is in the definition, not a theorem.)

If the opposite angles of a quadrilateral are congruent, then__________

…then the quadrilateral is a parallelogram.

Consecutive angles of a parallelogram are ____________.

Supplementary.

Always, Always, Sometimes, or Sometimes, or Never...Never...

The diagonals of a parallelogram ____ bisect each other.

Always

A quadrilateral is _____ a parallelogram,

Sometimes

The End