Geometry Flashcards
What do the exterior angles of a triangle add to?
360
What do the interior angles of a triangle add to?
180 Degrees
What is the area of a triangle formula?
Area = (1/2)(B)(H)
What is the Pythagorean theorem?
A^2 + B^2 = C^2
What is an equilateral triangle?
All sides are equal. All angles = 60 degrees. When an equilateral triangle has an angel bisected it becomes a 30/60/90 triangle.
What is an isosceles triangle?
Two sides are equal and two angles are equal
What is area of a circle?
Area = (pie)(r^2)
What is the circumference of a circle?
Circumference = (pie)(D) = 2(pie)(r)
What do you need to find the arc-length or arc degree of a circle?
The degree of an arc/360 is proportional to the area and circumference of a circle
What is the relationship between a radius and a diameter?
(2)(radius) = diameter
What are the total degrees in a circle?
360
What is the volume of a rectangular solid?
Base times height
What do two angles on a line equal?
180 degrees
What do angles around an intersection of at least two lines add to?
360 Degrees
Do parallel lines ever cross?
Not on a 2D plane. Not if they are on the same plane.
If a triangle is inscribed inside a circle so that one side of the triangle is a diameter. What type of triangle is it?
A right triangle.
If given a radius of a circle what can you determine?
Circumference, diameter, area. All other necessary values on the GMAT
What is a tangent line?
A line that touches a circle on exactly one point. It’s perpendicular to the radius at the point if tangency.
What axis is vertical?
Y axis
What axis is horizontal
X axis
What is the slope formula?
Rise/Run - (Y1 - Y2)/(x2 - x1) - (Delta Y / Delta X)
How are points written?
(X, Y)
What is the line formula?
Y = mx + b
M is slope
B is y intercept
(X,y) is a point on the line
What is the theory of triangle sides?
Two sides added together are always longer than the third side. The difference of any two sides is less than the third side.
Area if a rhombus?
A = (b)(h)
Area of a trapezoid?
A = (1/2)(b1 + b2)(h)
What is pie?
Circumference/Diameter. Infinite # 22/7 is close. 3.14 is also close.
What is 0/x =
Zero slope/Horizontal line
What is a 0 slope look like?
A horizontal Line
What does an undefined slope look like?
Vertical line. X/0
What is the slope of a vertical line?
Undefined/No Slope - Cannot divide anything by 0. (X/0 = Undefined)
Name two unique degree combinations in right triangles and the corresponding sides.
45: 45:90 X:X:Xsq.2
30: 60:90. X:Xsq3:2X
What are the two common Pythagorean triples?
3: 4:5
5: 12:13
x:12:13
5:12:13
5:x:13
5:12:13
5:12:x
5:12:13
What happens when you draw a diagonal in a parallelogram?
You bisect the area and if you have two lines they bisect each other
Def: Paraelleogram
Closed quadrilateral with two sets of parallel lines. Rectangles, squares, rhombus.
Volume of a rectangular solid?
V = (l)(w)(h)
Surface area of a rectangular solid?
SA = 2( lw + lh + wh) (the faces)
Volume of a cylinder?
Base x height. = (pie)(r^2)(h)
Surface area if a cylinder?
SA = (faces)(lateral surface area) SA = ((2)(pie)(r^2)) + ((2)(pie)(r)(H))
What is the lateral surface area?
Surface area of the cylinder height only. Does not include the faces. LSA=(circumference)(height)
Area of a Parallelogram?
Area = (b)(h)
Interior angles of a parallelogram add to?
360 degrees
How many sides does a polygon with 360 degree angles have?
4 sides
Area of a trapezoid?
Area=(1/2)(b1 +b2)(h)
How many sides are parallel in a trapezoid?
At least one set. If it’s two sets of parallel lines it’s a parallelogram.
Are all trapezoids parallelograms?
No
Are all parallelograms trapezoids?
Yes
Describe the height of a triangle
Distance from base to opposing apex. Must be perpendicular to base. Any side can be a base.
A 45:45:90 triangle is 1/2 a what?
Square
When an altitude is drawn from the unequal side of an isosceles triangle is does what?
Bisects the base and the angle.
What does congruent mean?
Equal
Every equilateral triangle is also what type of triangle?
An Isosceles triangle. All isosceles triangles are not equilateral triangles.
What does the height of an equilateral triangle always equal?
(Sq root 3)(x)/(2)where x is the side of the triangle.
What is a chord?
A line connecting two points in a circle that doesn’t necessarily go through the center of the circle.
Describe a diameter in terms of a chord.
A chord that goes through the center of a circle.
What is a central angle?
An angle that starts in the center if a circle.
What is an inscribed angle in a circle?
It’s inside the circle and it starts from the circumference as opposed to a central angle that starts in the center of a circle.
If multiple inscribed angles in a circle share the same arc describe the angles.
They are all equal to one another if they share the same arc and they are all inscribed.
Describe the relationship of a central angle and an inscribed angle share the same arc.
The central angle is twice the inscribed angle. The inscribed angle is half the central angle.
What can you find if you have an inscribed angle and a radius?
All of it! Area/circumference/length arc.
What’s the slope of parallel lines?
The same.
What’s the slope of a perpendicular line?
The negative reciprocal of the other line.
If you increase the slope what happens to the line ?
It gets steeper.
What’s the direction of a positive slope?
Northeast
What’s the direction if a negative slope?
Southeast
Describe the quadrants in coordinate geometry.
Starts in the (pos,pos) quadrant with 1 and then moves counter clockwise.
How do you find the x intercept?
Set y to zero or use the formula = (-b)/m
Describe the slope of two lines if the product of them equals -1.
They are perpendicular.
What is the distance between two points?
=sq root{(x1 - x2)^2 + (y1 - y2)^2}
Midpoint formula?
={(x1 + x2)/2, (Y2 + y1)/2}
How do you determine the number of degrees inside a polygon?
=(n-2)(180) where n=the number of sides
What is a rhombus vs trapezoid?
Rhombus - Two sets of parallel lines without right angles. Trapezoid - One set of parallel lines in a quadrilateral. All parallelograms are trapezoids.
Describe a major vs a minor arc.
The minor arc is the smaller arc. The major arc is the other/outer arc.
What are uniform solids?
If you cut them into cross sections that would have the same bases as the original.
What is a vertex? What is he plural version of this?
A corner in a polygon. Plural: Vertices
What are supplementary angles?
The add to 180
What are complementary angles?
Add to 90 degrees
What are bisected angles?
An angle that is split evenly.
What are adjacent angles?
The are next to each other on a straight line.
Area of a parallelogram
Area = (base)(height)
What are vertical angles ?
Just like it says. If two lines cross they are he angles across from each other.
What is a transversal?
A line that crosses parallel lines.
What is the origin?
Point (0,0) on coordinate geometry.
What is the altitude?
The height
Describe legs/base in a triangle.
There are two legs and 1 base.
How many sides in a pentagon?
5
How many sides in a hexagon?
6
What is a semicircle?
Half a circle. A circle cut by its diameter
What is the exterior angle of a triangle equal to?
The sum of the other two interior angles.
What is a regular polygon?
A polygon with equi-angles and equi-sides.
What is a polygon?
A closed plane figure formed by three or more line segments.
What makes triangles congruent?
Equal angles and equal sides. Basically, equal triangles.
Sometimes the height of a triangle is outside of the triangle.
72 degrees
1/5 a circle
1/6 a circle
60 degrees
