Geometry Flashcards
Can you assume lines to be straight?
Yes
Can you assume lines to be perpendicular or parallel?
No
When are shapes congruent?
When they are of the same size and shape. Orientation does not matter.
If a line bisects a line and is perpendicular to it
Every point on the perpendicular bisector of a segment is equidistant from the two endpoints of the segment.
Supplementary
180
Compelmentary
90
Sum of angles of a triangle
180
Acute angles
At least two of the angles in a triangle have to be acute
Largest angle always opposite
The longest side.
The sum of two sides of a triangle
Greater than the third side
The difference between the two sides of a triangle
Smaller than the third side
The third side
Greater than the difference and less than the sum
Can you assume that lines/angles that look similar or of the same length that they are?
No
Assuming for problem solving
Figure is always drawn to scale so we can assume that two angles are similar or close to one another by just looking at them; we can also assume the angle measurements; just visual ESTIMATION
Assuming for data sufficiency
Not always drawn to scale just use the information blatantly given to us
For all the diagrams
Look big and look small (specially for triangles)
Two way theorem-Isosceles triangle
Two angles opposite equal sides are equal
Equilateral triangle
Three equal 60 angles and three equal sides
Height
Segment from a vertex to the opposite side that is perpendicular*
Base
Whatever side the height is hitting
Right triangle area
Product of the two legs
All three sides can be used as a base but
They all give you the same area
Median
Line that goes from a vertex to the midpoint of the opposite side. Only divides that opposite side in half but does not divide the angle.
Angle bisector
Divides the angle in half but not the opposite side.
In an isosceles and equilateral triangle
The line from the non equal angle to the opposite side= divides the angle into two equal angles, is perpendicular to the base, divides the base into half, if one segment is playing more than one role= isosceles; divides into two congruent right triangle;
Pythagorean triplet
3,4,5; 5,12,13; 8,15,17; 7,24,25; GCF times final answer
Congruent Shapes
Same shape and same size= basically equal
Similar shapes
Same shape but different sizes
Similar triangles
All angles are equal, (or know that two angles are equal
Similar triangles sides
Are proportional
In similar triangles
Any lengths are smaller triangle times scale factos
Similar triangles and the idea of scale factor
k
Area of similar triangles
Scaled up by ksquared
Halving and Doubling
Anything with 5 in the units digit double that and half the other one
45-45-90 triangle
1:1: root two; we get this when we divide a a square into two along one or both of its diagonals
30-60-90
1: root 3: 2
Area of an equilateral triangle
root 3 over four s squared
Sum of angles of a quadrilateral
360
Every quadrilateral, diagonals
Exactly two
Parellelogram
Opposite sides and angles are equal, sides are parellel, diagonals bisect each other; if any one of them is true all others are true
Rhombus
Diamond, four equal sides, they are parallelogram, + all four sides are equal and diagonals are perpendicular (these diagonal properties can be true for other irregular quads)
Rectangle
Special properties apart from the parallelogram: diagonals are congruent, not unique to rectangles
Square
Parallelogram; rhombus, and a square
Trapezoid
One set of parallel; if it is an isosceles trapezoid, then the non parallel sides are equal, opposite side angles are equal and diagonals are equal
Length of a slanted line
Pytha
Symmetrical trapezoid
Can divide into rectangle and two triangles on each side
Area of a rhombus and a paralellogram
B*H where h is the altitude
Area of a trapezoid
h * average of bases or divide it into two triangles and a rectangle**
Diagonals pentagons
Five
Hexagon diagonals
Nine
Sum of angles for polygons
(n-2)* 180
Regular polygon
Equal sides and equal angles; if a diagonal bisects the whole shape, it bisects the angle
Pie
22/7
Equal central angles
Equal arcs and equal chords
Inscribed Angle
Vertex on the circle, inscribed angle is half the central angle and the arc
If two different angles are drawn from the same chord
Then those two angles are equal; if they are on the same side of the chord
If an angle is drawn from two end points of a diameter
90 degree angle
Angle between radius and tangent point
90 degree
Trick
Find the chord
Space diagonal cuboid
one point to the opposite point of the other side
l squared + hsquared + b squared
Space diagonal cube
square root of 3 a
Cylinder volume and height
Volume= piersquaredh (base times height)
Surface area:2piersquared+ 2pierh
Sphere
Every point is equidistant from the center; volume= 4/3 piersquaredcubed
Area: 4*pirsquared
