ma.8.g.2.2 classify and determine the measure of angles, including angles created when parallel...

MA.8.G.2.2

Classify and determine the measure of angles, including angles created when parallel lines are cut by transversals.

Block 25

Teacher Quality Grant - AE - FAU 2

Some History

The history of the mathematical measurement of angles, possibly dates back to 1500BC in Egypt, where measurements were taken of the Sun's shadow against graduations marked on stone table.

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What does the word Degree mean?

Position on a scale

Based on Latin De - down Gradus - step or

grade

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Why 360° in the Circle?• Probably based on the fact that 360 is

approximately the number of days in a year.

• Its use is often said to originate from the ancient Babylonians (1696 – 1654 BC). Ancient astronomers noticed that the stars in the sky seem to advance in a circular motion by approximately one-360th of a circle, i.e., one degree, each day.

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Subdivisions of Degrees

• One degree is divided into 60 minutes (of arc)

• One minute is divided into 60 seconds (of arc)

• Another indication of the Babylonian influence

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Example on Earth• Longitude is the angular distance, in degrees,

minutes, and seconds, of a point east or west of the Prime (Greenwich) Meridian.

• If you divide the circumference of the earth (approximately 25,000 miles) by 360 degrees, the distance on the earth's surface for each one degree longitude is just over 69 miles, or 111 km.

• There are 24 standard time zones defined by using the meridians. How many degrees between each time zone?

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Divisors of 360• 360 has 24 divisors, including 1 and

360• Can you find all the divisors?• The divisors include every number

from 1 to 10 except 7• For the number of degrees in a circle

to be divisible by every number from 1 to 10, how many degrees would the circle need?

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Vocabulary

In everyday language:• Obtuse means not alert in perception

or intellect• Acute means sharp• Supplementary means additional• Complementary means completing

Do the everyday meaning of these words relate to their mathematical meaning?

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Vertical - Adjacent AnglesOpen the GeoGebra file vertical_adjacent

1. Name some facts about the observed angles in figures 1, 2, and 3

2. What are congruent angles?3. What figure shows vertical angles?4. What figure shows adjacent angles?5. Is it enough to define vertical angles as opposite

angles?6. Is it enough to define adjacent angles as next to each

other?7. What would be an accurate definition for vertical

angles and adjacent angles?

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Students Confuse…• Adjacent angles• Linear pair• Supplementary angles– Draw examples of each one or create a

GeoGebra file that shows clearly the difference between them.

– How can we help students understand and remember the difference between them?

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Corresponding Angles

• Open the GeoGebra file corresponding1• Move point A and notice the different pairs

of corresponding angles• Overlap point A with point B and move the

point on the slider to the left. What do you notice?

• How can this file help teach this concept to the students?

• Could you make a similar file to show the definition for Alternate Interior angles?

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Corresponding Angles

• Open the GeoGebra file corresponding2

• Move points A or B:–What do you notice?–What is the relationship between the

blue lines when the pairs of corresponding angles have the same measure?

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Interactive Website

http://www.mathopenref.com/anglescorresponding.html

Explore this website and its links to other angle relationships.

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Angles in a ClockOpen the GeoGebra file angles_clock1. How many degrees separate one number

from the next?2. How many minutes must pass for the hour

hand to move 1 degree?3. What is the angle measure between the

hour hand and the minute hand at 12:15?4. When after 3 o’clock will the angle between

the hour and minute hands be exactly 180°?

You can use a protractor to verify your answers

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ma.8.g.2.2 classify and determine the measure of angles, including angles created when parallel...

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