Geometry Flashcards
Line
connecting two points and extending indefinitely
Ray
half-line
Line segment
have two endpoints
Angle
union of two rays sharing a common endpoint
Acute angle
whose measure is more than 0 degree but less than 90
Right angle
exactly measures as 90 degree
Obtuse angle
the measure is more than 90 degree but less than 180 degree
Straight line
exactly 180 degree
Are the diagram drawn to scale
no - so an angle might be 1 degree or angle number 1
When n line intersect through a common point
the sum of all the angles created by those n lines ta that point is 360 degree
Intersecting line is perpendicualr
each angle formed between that line are a 90 degree
- two straight lines are said to be perpendicular when they intersect and form four right angles
Supplementary angle
angle that add up to 180 degree
Transversal line
two parallel lines cut by a line
When lines are cut by a vertical line
vertical angles are equal
Triangle add up to
180 degree
Largest angle of a triangle
opposite of the longest side of the triangle
Smallest angle
opposite of the shortest side of the triangle
Exterior angle
Given any polygon, when taking one exterior angle at each vertex, the sum of the measure of the exterior angles will always equal to 360
The measure of the two exterior angles of the triangle is equal to the sum of the measure of the
two remotes interior angles
altitude
height
In any triangle, the sum of the lengths of any two sides of the triangles is greatest than the length of the
third side
In any triangle, the difference of the lengths of any two sides of the triangles is less than the length of the
third side
scalene
no sides are the same
isosceles
two sides are the same
equilateral
all sides are the same
acute triangle
each of its side is less than 90 degree (can be scalene, isosceles or equilateral)
obtuse triangle
one angle is greater than 90 but less than 180 (can be scalene, isosceles)
right angle triangle
one angle is 90 degree (can be scalene, isosceles)
Pythagorean triple #2
5-12-13
- any factors/combination of this will be Pythagorean triple so {10-24-26}, { 15-36-39} and so on will be the triples
Pythagorean triple #1
3-4-5
- any factors/combination of this will be Pythagorean triple -> so {6,8,10}, { 9,12,15} and so on will be the triples
The area of an isosceles right triangle can be found using the formula
I^2/2 where I is the length of one of side
The side of a 45-45-90 right triangle are in a set ratio of
x, x, and xrad2 where x rad 2 represents the lengths of the hypotenuse and x represents the length of each of the shorter legs
A square diagonal cuts the square into
two 45-45-90 right triangles
The side of a 30-60-90 right triangle are in a set ratio of
Always exhibit the same ratio of x: xrad 3, 2x
Area of an equilateral triangle
(s square rad 3)/4
Cutting an equilateral triangle in half form
makes the triangle 30, 60, and 90-degree triangle
Two triangles are similar if
one triangle is simply an enlargement of another triangle
Triangles can be similar if (1)
three angles of one triangle are the same measure as three angles of another triangle
Triangles can be similar if (2)
three pairs of corresponding sides have lengths in the same ratio
Triangles can be similar if (3)
an angle of one triangle is the same measure as an angle if another triangle and the sides surrounding these angles are in the same ratio
Sum of Interior angle
180 (n-2), where n is the number of sides
Square
all sides are 90 degree
Rectangle
opposite sides are equal
Rhombus
all sides are equal
The perimeter of a semi-circle
not half of what the circle rather it’s -> pi(r)+2r
A measure of central angle is always half the
measure of the central angle
Arc Length
2(pi)(r)(C/360); where C is the central angle and
Area of sector
(pi)(r^2)(C/360), where C is the central angle
