isee prep geometry - weebly
TRANSCRIPT
The perimeter of a polygon is the sum of the lengths of the sides. The perimeter
of the shape above is 5 + 7 + 3 + 8 =23 A rectangle is a polygon with four right angles. Opposite sides are congruent. The
perimeter can be found by using the formula
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P = 2 l + w( ) . A square is a rectangle with four congruent sides. The perimeter can be found by
using the formula
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P = 4s . A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides
and angles are equals. A trapezoid is a quadrilateral with one pair of parallel sides. The area of a polygon is the number of square unites needed to cover the surface.
Area = (length)(width) Area = side2 Area = (base)(Height)
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A = lw
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A = s2
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A = bh
Area = half of height times the sum of the lengths of the parallel sides.
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A =12h a + b( )
In the above figure the area is
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12⋅5 4 + 9( ) or 32.5 square units.
If two polygons are similar, then the corressponding angles are congruent and the
corresponding sides are proportional. In the above, the two rectangles are
proportional because
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64
=128. The larger triagle is 1.5 times larger than the smaller
sides.
A circle is a closed figure where each point is equal distant from the center. In the
picture, O is the center. The radius of a circle is distance from the center of the circle to any point on the
circle. In the drawing the radius is
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OA .
A chord is a line segment that connects any two pints on a circle. In the drawing
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AB and
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AC are chords. The largest chord in a circle is the diameter.
The diameter is a chord that goes through the center of the circle and is twice the length of the radius. The circumference of a circle is the distance around the circle. It can be
calculated by using the formula
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C = 2πr or
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C = πd .
π is the ratios of the circumference to the diameter;
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π =Cd.
For most calculations , 3.14 is the standard approximation. Sometimes the answer will not be an approximated answer. In this case the answer is left in terms of π. See example below. The area of a circle is
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A = πr2 . Since the formula is asking for the length of the radius to be squared, if given the diameter you must divide by two to get the radius before applying the formula. For example if the diamter is 12, then the radius is 6.
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A = π ⋅62 or 36π
In the above diagram, the perpendicular lines are the coordinate axes in a
coordinate plane. The horizontal line represents the xaxis, the vertical line represents the yaxis and 0 represents the origin (0,0). Ordered pairs are numbers which specify a specific location within the coordinate plane. These coordinates come in the form (x,y) where x is the first coordinate that moves with the x‐axis and y is the second coordinate that moves with the y‐axis. Starting from the origin, the x value moves right when positive, left when negative, while the y value moves up when positive and down when negative.
A number in the lower right corner would have a positive x value and a negative y
value.
To use an equation to find the slope, put the equation in the slope‐intercept form
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y = mx + b where the slope is m . To find the slope of the equation
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6x + 3y = 9 , adjust the equation so that it is in point slope form.
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6x − 6x + 3y = 9 − 6x sub 6x from both sides – Sub Prop of equality
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33y =
−63x +
93 isolate the y by dividing both sides by 3
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y = −2x + 3 Slope‐intercept form
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∴ the slope is ‐2.
To find the length of a line segment parallel to the x‐axis, calculate the differences
of the absolute value of the x‐coordinate. To find the length of a line segment parallel to the y‐axis, calculate the differences of the absolute value of the y‐coordinate.
To determine if a geometric figure can be retraced without lifting a pencil follow
the following rule: In any given figure, if exactly zero or two points have an odd number of
intersecting line segments/ and or curves, it can be drawn without lifting the pencil.