Geometry Flashcards
Area of a Triangle
area = ½ base × height
Angles in a Triangle
All angles in a triangle
sum to 180
x + y + z = 180
Pythagorean Theorem
In a right triangle, a2 + b2 = c2,
where a and b are the legs
(shorter sides) and c is the
hypotenuse.
Pythagorean Triples
The most common triples are 3–4–5,
5–12–13, 7–24–25, and 8–15–17.
Similar Triangles
Similar triangles have all the
same angles, and sides that
are proportionate.
Third Side Rule
The third side of a triangle is greater than
the difference of the other two sides and
less than their sum.
(a + b) > c > (b − a)
Angle/side Relationship
Side length corresponds with
angle size. Angle z and side c are
the largest. Angle x and side a
are the smallest.
Special Right Triangles
Isosceles and Equilateral
equilateral = all sides are the same length
isosceles = two sides are the same length
In an equilateral triangle, all angles are 60°.
Area of a Rectangle
area of a rectangle = length × width
area of a square = side2
Area of a Parallelogram
area of a parallelogram = base × height
Sum of Angles in a Polygon
sum of angles in a polygon = 180(n − 2),
where n = number of sides
Volume and Surface Area of a Box
volume = l × w × h
surface area = 2lw + 2wh + 2lh
Volume and Surface Area
of a Cylinder
volume = πr2h
surface area = 2πr^2 + 2πrh
Lines and Angles
All angles in a line add up to 180°
x + y = 180
Parallel Lines
When a line intersects with two parallel angles, the resulting intersections are identical.
Intersecting Lines
When two lines intersect, opposite angles are equal.
Distance and Midpoint on a Coordinate Plane
If you have endpoints (x1, y1) and
(x2, y2) of a line on a coordinate plane:
Sector
Sector area and arc length are proportional to angle size. Here, the angle is 60°.
Since there are 360° in a circle, the sector (grey area) takes up 1/6 of the circle. Thus,
its area is 1/6 of the total area, and its arc length is 1/6 of the circumference.
Slope, x-, y-intercept
y = mx + b, where m = slope, b = y intercept
slope = rise/run or (y2-y1)/(x2-x1)
The y-intercept is the y-coordinate on
a line at which x = 0.
The x-intercept is the x-coordinate on
a line at which y = 0.
Circles Facts
diameter = 2r
circumference = πd or 2πr
area = πr2
Central Angle (circles)
A central angle has a vertex that
lies at the center point of the
circle. An inscribed angle has its
vertex on the circle itself rather
than on the center of the circle.
An inscribed angle is equal to
half of the arc it intercepts.
Triangles in Circles
If one of the sides of an
inscribed triangle is a diameter
of the circle, then the triangle
must be a right triangle.
Coordinate Plane
- Slope: (change in y / change in x) (rise / run)
- Slope-intercept: y = mx + b
- “Line contains point” means you could plug a coordinate pair, f.e. (5, d)
into a line, f.e. y = 3x + 4, by replacing x = 5 and y = d … d = 3(5) + 4 - parallel lines (do not intersect … same slope)
- perpendicular lines (slope is opposite reciprocal .. the product of their
slope is -1) - finding distance between two points (make a right. triangle where the
distance is the hypotenuse)
