Symmetry and Similarity

• At the right is a multiplicationtable with only the ones digitshowing.

• Describe any rotations, translationsreflections…

• Finish work: webegin in 10 minutes.

1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9

2 2 4 6 8 0 2 4 6 8

3 3 6 9 2 5 8 1 4 7

4 4 8 2 6 0 4 8 2 6

5 5 0 5 0 5 0 5 0 5

6 6 2 8 4 0 6 2 8 4

7 7 4 1 8 5 2 9 6 3

8 8 6 4 2 0 8 6 4 2

9 9 8 7 6 5 4 3 2 1

Tessellations, briefly• This is sometimes called “tiling” the

plane.

• A figure is repeated in such a way that there are no overlaps and no gaps.

3

2 13

21

How can you tell?• Take any quadrilateral, then rotate it,

180˚. Make some copies of these.

• Now, put them together.

In general• The sum of the angles about a point

must total 360˚.

• So, question: will every convex quadrilateral tessellate?

• Will regular hexagons tessellate?

• Will regular octagons?

Similarity• Do exploration 9.1 part 3 on page 239.

• Using geoboard paper draw TWO similar figures for a, b, d, f, and g only.

• Write a definition or a detailed description of what makes two figures similar.

Similarity• Figures that are similar have corresponding

parts--– The corresponding angles are congruent.– If each of the corresponding sides is also

congruent, then the two figures are congruent.– If each of the corresponding sides are in the same

proportion, then the two figures are similar.– If even one pair of corresponding sides is not in

the same proportion, then the figures are not similar.

Just a refresher• How do we write this?

ORL

K J

I

HG

F

E D

C

BA

Q P

NM

Congruent vs. Similar

Find missing lengths

3

4.5

7

7

3

y1

x7

• If the sun shines on a 6 foot man creating a 10 inch shadow, how long will the shadow be of a 40-foot cactus?

Not to scale

Measurement, Perimeter, Area

• In your groups, make a list of:

– All the measurement conversions you know;

– All the perimeter and area formulas you know.

What is measurement?• A measurement is determined by the number

of repeated units needed to fill a specific length, time, area, volume, weight, capacity, temperature, etc.

• The units we are accustomed to using are inches, seconds, square feet, cubic centimeters, pounds, tablespoons or Liters, degrees Fahrenheit, etc.

Systems of Measurement• Time:

• Length:

• Liquid Capacity:

• Dry Capacity:

• Weight:

• Temperature:

Conversions you should know!

• 3 teaspoons = 1 tablespoon;• 2 tablespoons = 1 liquid ounce;• 8 liquid ounces = 1 cup;• 2 cups = 1 pint; 2 pints = 1 quart; • 4 quarts = 1 gallon• 16 ounces = 1 pound; • 2000 pounds = 1 ton.

Conversions you should know!

• 60 seconds = 1 minute; • 60 minutes = 1 hour; 24 hours = 1 day• 12 inches = 1 foot; 3 feet = 1 yard;• 5280 feet = 1760 yards = 1 mile• Freezing: 32˚F = 0˚C; Boiling: 212˚F =

100˚C; Random: -40˚F = -40˚C

Metric vs. CustomaryKilo Hecto Deka Unit Deci Centi Milli

meter Liter gram

As you move to smaller units, there are more per unit, so multiply by 10.

As you move to larger units, there are fewer per unit, so divide by 10.

Ex: 56 mm = _____ m; 95 kg = _____ g; 39 L = _____ mL

Common Conversions• 1 inch is exactly 2.54 cm• 1 meter is about 39 in.• 1 mile is about 1.6 km• 1 kilometer is about 0.6 miles• 1 mL is about 1/4 teaspoon of water• 1 Liter is about a quart.• 1 mg is about the weight of a strand of hair.• 1 gram is about the weight of a raisin or small

paperclip.• 1 kilogram is about 2.2 pounds.