Geometry Flashcards
When n lines intersect through a common point, the sum of the angles created by the those n lines is…
360
Angles are supplementary if..
Angles are supplementary if their measures add up to 180°.
For triangles, the longest side of the triangle is always opposite…
the largest angle
For triangles, the shortest side of the triangle is always opposite…
the smallest angle
Sum of several exterior ADJACENT angles of a polygon must equal…
NOT mirroring angles
360
taking one exterior angle at each vertex. if more than one, treat each additional as another part of a 360 add up
An exterior angle of a triangle is equal to the sum of the two remote interior angles
‘remote’ angles are those that are not immediately next to exterior angles
Sum of lengths of any two sides of a triangle must…
Be greater than the length of the third size
A + B > C
B + C > A
A + C > B
Difference of lengths of any two sides of a triangle must…
Be less than the length of the third size
A - B < C
B - C < A
A - C < B
Acute angle is
less than 90 degrees
obtuse angle is
greater than 90 degrees but less than 180
Two most common pythagorean triples
3-4-5 [incl any multiples such as 6,8,10 and 9,12,15]
5-12-13 [incl any multiples as as 10,24,26]
what are the angles of an isosceles right triangle
45-45-90
2 legs are equal
area = leg^2/2
Ratio of sides of 45-45-90 right triangle [iscoeles]
x : x : x√2
where x is the length of the two equal legs, x√2 is hypotenuse
if we know the size of one leg, we can determine the size of all legs
Ratio of sides of 30-60-90 right triangle
x : x√3 : 2x
x = side opposite of 30 degree angle
x√3 = side opposite of 60 degree angle
2x = side opposite of 90 degree angle
if we know the size of one leg, we can determine the size of all legs
Area for equilateral triangle
Area=s^2√3/4
where s is one size
the area can only be determined only when the height is known
What are quadrilaterals?
four sided polygons, including squares, rectangles, parallelograms, rhombuses, and trapezoids
all squares are rectangles, all rectangles are parallelograms
what is the equation for the diagonal of any rectangle?
√l^2+w^2
Properties of a square
- 4 right angles
- 4 sides of equal length
- each diagonal bisects the square into 2 45-45-90 triangles
- length of square’s diagonal [hypotenuse] = s√2 where s is the length of one side of square
Given a rectangle with a fixed perimeter, the rectangle with the maximum area is a square.
Given a rectangle with a fixed perimeter, the rectangle with the maximum area is a square.
Given a rectangle with a fixed area, the rectangle with the smallest perimeter is a square.
Given a rectangle with a fixed area, the rectangle with the smallest perimeter is a square.
Trapezoid
Trapezoid is a quadrilateral where the bases are parallel but the other pair of opposite sides are not parallel
area of a trapezoid
(base 1 + base 2) * height / 2
sum of interior angles of a polygon
sum of interior angles of polygon = (n-2) x 180
where n = number of sides
measure of any one interior angle in a polygon
180(n-2)/n
