Flashcards in Geometry Deck (32):
Bisecting line` `
Splits something into 2 EQUAL parts`
Be aware that polygons do not have to...
Regular = all sides the same lengt
Sum of interior angles of a triangle
Add up to 180
Sum of interior angles of a quadrilateral (4 sides)
Add up to 360
The sum of the interior angles of every pentagon (5 sides)
Add up to 540
Hexagon - sum of interior angles...
...add up to 720
Sum of interior angles of any polygon =
Sum of exterior angle and interior angle...
...always equals 180
Num of interior angles and exterior angles in every polygon
Is equal (triangle has 3 interior angles, that add up to 180, and 3 exterior angles)
The sum of the exterior angles of ANY polygon...
...is always equal to 360
For triangles - an EXTERIOR angle of a triangle is always equal to....
...the SUM Of the NON-ADJACENT interior angles.
...that the lines are parallel, angle is right, shape is a square, etc. (Unless the exam explicitly states otherwise)
Tricky problem with lines and angles...
1. Draw the diagram
2. Look for relationships you know
3. Don't be afraid to "tune out" lines temporarily
4. If you can find >1 equation , COMBINE equations using subtraction or elimination
5. Look back at the diagram to see if your solutions make sense with the general shape
Label ALL of the interior (or exterior) angles of the polygon, using 180-x
2 angles of = measure, 2 sides of = measure.
NOTE - an equilateral is just a SPECIAL type of isosceles.
3-4-5 (6-8-10; 9-12-15; 12-16-20; 15-20-25)
45-45-90 triangles [isosceles right triangle]
x:x:x(sq.rt of 2)
CUT the hypothenuse in HALF and MULTIPLY the result by sq. root of 2
Every equilateral triangle
Is composed of TWO 30-60-90 triangles
Perimeter and triangle inequality theorem
Sum of any two sides of any triangle must be greater than the third side. Conversely, the difference of any two sides must be less than the third.
LESS THAN THE SUM, BUT GREATER THAN THE DIFFERENCE
Parallelogram - adjacent angles
Always add up to 180
Diagonals of a parallelogram...
...bisect one another and split the shape into two equilateral triangles
Area of a parallelogram
Is equal to BASE times HEIGHT
Area of a trapezoid
Average of bases x height
Units in a surface area question...
...should be squared
Volume of a rectangular solid
Length x Width x Height
Units when calculating volumen...
Should be cubed
How to determine the interior diagonal of a rectangular slid?
The Diagonal of a Rectangular Solid = square root of (lˆ2 + wˆ2 + hˆ2)
Diagonal of a Cube
Diagonal of a Cube = s (square root of 3)
S = side length
To find the midpoint if you know the two coordinates
Average the x-coordinates and y-coordinates
The product of their slopes = -1