## Geometry Concepts:GRE°

##### Created by:

isaidy  on October 25, 2012

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GRE Geometry concepts

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# Geometry Concepts:GRE°

 ∏ =3.14
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#### Definitions

∏ = 3.14
√2= 1.4
√3= 1.7
The point of intersection for an angle is a vertex
the sum of the measures of the angles on one side of a straight line = 180°
the sum of the angles around a point = 360°
supplementary angles make a straight angle 60° +120°=180°
complementary angles make up a right angle 30° +60°=90°
bisect means to split a line or angle into two equal lines or angles
verticle angles are opposite angles of two intersecting lines
each verticle angle is supplementary to each of its adjacent angles
When two parallel lines intersect with a third line all acute angles formed are equal, all obtuse angles formed are equal, and any acute angle is supplementary to any obtuse angle
If a line gets higher as you move to the right, it has a ______ slope positive
If a line goes down as you move to the right, it has a _______ slope negative
Slope = rise/run = change in y / change in x
Rise means the differnce between the y-coordinate values of the two points on the line
Run means the difference between the x coordinate values of the two points on the line
Slope intercept form is y=mx + b (m is the slope, b is the y intercept point)
Triangle angles = ______° 180
Altitude = height of a triangle
The length of any side of a triangle is _______ than the sum of the other two sides less
In triangles, the greater angles lie opposite the _______ ______. longer sides
Area of a triangle = 1/2 base x height
Area of a right triangle= 1/2 lenght1 x length2
Perimeter of a polygon= distance around the polygon
Isosceles triangle are triangles that have two sides (and hence two angles ) that are equal.
Equilateral triangles are triangles that have three sides (and three 60° angels) othat are equal.
Similar triangles are the same shape
Congruent triangles are the same shape and size
The ratio of the areas of two similar triangles is the SQUARE of the ratio of the corresponding lengths
Right triangles have 2 legs (a and b) and a hypotenuse (c)
Pythagorean theorum states a² + b² = c²
Pythagorean triplets are right triangles with sides 3,4,5 (6,8,10, or 9,12,15)and 5,12,13 and 7,24,25 and 9,40,41 and 11,60,61
Pythagorean special combos are right triangles with sides 1,1,√2 for isosceles right) and 1,√3,2 (for 30,60,90 triangles)
Quadrilateral is a four sided polygon with angles that equal 360°
For Squares: Area = side squared or √Area = side
For similar figures: The ratio of areas = the ________ of the ratio of lengths square (ex. 25/36 =5sq./6sq.)
Area of a circle = ∏r²
A chord is a line segment joining 2 points on a circle
A line drawn tangent to a circle is is perpendicular to the radius at the point of tangency
A circumference of a circle = ∏d or 2∏r
∏ is the ratio of the circle's circumference to it's diameter or C/D
An arc is a portion of the circumference of the circle and equals the degrees of the angle
A minor arc is the small arc of a circle. A major arc is the _____ arc of a circle larger
Arc length = (angle/360°)(circumferance) or angle/360° x 2∏r
A sector is a pie shaped portion of a circle
Area of a sector=(angle°/360°)(∏r²)
Inscribed shapes are inside another shape and all the vertice touch the edge of the outside shape
Circumscribed shapes are outside another shape and all the vertices touch the edge of the inside shape
A triangle circumscribed in a half circle is a ________ triangle right

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