Lesson 1 Intro to Polygons P5...

Lesson 1 Intro to Polygons P5 2014.notebook

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May 07, 2014

Properties Of Quadrilaterals And Polygons


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Roofers use properties of Polygons?

A roofer must determine if a roof is "square" before they install shingles. "Square", in construction terms, means that the corners have true 90° angles. A roofer wants the shingles to line up straight as seen from the ground, so it is important to make sure that the roof is not a parallelogram but a rectangle. To figure that out, a roofer will use polygon properties and measure the diagonals of the roof. If the diagonals are equal, the roof is rectangular. The roofer can then begin his starter strip along the edge followed by the shingles. Also, where the diagonals cross in a rectangle will be the exact center of the roof. Some roofers will use that center point as a guideline to lay the first shingle.


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May 07, 2014

Labeling Angles


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Angle RulesRule 1: Complementary AnglesIf two angles add to 90°, you say they are complementary to each other. Or you could also say one is the complement of the other.

Example 1Are AOB and BOC complementary?


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Rule 2: Supplementary AnglesIf two angles add to 1800 , you say one is the supplement of the other.

Example 1Are AOC and COB supplementary?


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Rule 3: Corresponding AnglesA transversal is a line that intersects two or more lines. The lines may or may not be parallel. Corresponding angles are located in similar positions with respect to the parallel lines.

1 and 2 are both located to the left of the transversal and on top of the parallel lines.


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Rule 4: Vertically Opposite AnglesAny time two lines intersect, 4 angles are formed.


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Find measures of x, y, z


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Rule 5: Alternate Angles


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Find measures of A, B, and C


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Find measure of 1:


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The lines are parallel and cut by a transversal. 2 corresponds with the angle whose measure is 120剸.

Thus, 2 = 120剸


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Give a reason why 3 = 110.

The lines are parallel. 3 is an equal interior alternate angle to the angle whose measure is 1100 .

3 = 110


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The lines are parallel. 4 is an equal exterior alternate angle to the angle whose measure is 135 0 .

4 = 1350 .

Find measure of 4:


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Since any two intersecting lines make equal vertically opposite angles, 5 is 50. The pairs of lines do not have to be parallel for this to be true.

Find measure of 5:


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You are given that AB is parallel to CD and 5 = 80.

4 = 80 interior alternate to 5 7 = 100 supplementary to 5 8 = 80 vertically opposite to 5 3 = 100 corresponding to 7 2 = 100 vertically opposite to 3 1 = 80 corresponding to 5 6 = 100 corresponding to 2


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Properties of PolygonsA polygon is a figure formed by three or more segments (sides).

Convex polygons are polygons in which each interior angle measures less than 180°. In other words, the polygon does not "cave" in on any side.

Concave polygons, one or more interior angles may measure more than 180°.

Convex: Concave:

In a regular polygon, all sides are equal in length and all angles are the same measurement.


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May 07, 2014

Interior Angle Properties of PolygonsThe sum of all interior angles in a convex polygon can be found by using the formula:Sum = 180°(n − 2)Where n = the number of sides of the polygon.

Example 1:

Find the measurement of all the interior angles in a regular polygon with 5 sides.

Example 2:

Find the measurement of one of the angles in the regular 5sided polygon.


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Exterior Angle Properties of PolygonsThe sum of all measures of the exterior angles in a regular polygon equals 360°. Therefore, to find the measure of one exterior angle, divide by n.

Example

Find the measurement of the exterior angle of a regular 5sided polygon.

It is important to note that you just discovered that a 5sided polygon has interior angles which each measure 108°.Together, the interior angle (108°) and the exterior angle (72°) add up to 180°.


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May 07, 2014

Polygons in Construction

Find the measures of the interior and exterior angles in a STOP sign.


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May 07, 2014

3. Evaluate: 24

4. Determine the next two values in this pattern: 3, 6, 12, __, __.

5. Evaluate: 6 + 5(4 − 2) ÷ 2

1. Find the mean of these numbers: 4, 5, 8, 10

2. Calculate the perimeter of this rectangle:

MENTAL MATH

Lesson 1 Intro to Polygons P5...

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