Geometry Flashcards
When one shorter side of a right triangle has a length of (a multiple of) 3 and the other shorter side has a length of (a multiple of) 4, what must the length of the hypotenuse be (a multiple of)?
(A multiple of) 5
3-4-5 right triangle
When one shorter side of a right triangle has a length of (a multiple of) 5 and the other shorter side has a length of (a multiple of) 12, what must the length of the hypotenuse be (a multiple of)?
(A multiple of) 13
5-12-13 right triangle
What is an isosceles triangle?
What is an isosceles right triangle?
A triangle that has 2 equal sides and 2 equal angles.
An isosceles right triangle has two equal sides and two equal angles that each measure 45 degrees. The third angle measures 90 degrees.
What are the two shorter sides of a right triangle?
The legs - also the base and the height of the triangle
What is the area of a triangle?
(base x height) / 2
What is the area of a right triangle?
What about the area of an isosceles right triangle?
(Leg 1 x leg 2) /2
(Leg^2)/2 -> since the legs are the same length
The sides of a right isosceles triangle (or 45-45-90 triangle) will always be in what ratio?
x, x, root 2* x
What’s important to know when asked to find the diagonal of a square?
The diagonals of a square cut the square into two 45-45-90 right triangles. The area of each of these triangles is half of the area of the square that they form. Thus if you are given 1 side of the square, you can find the length of the diagonal.
The sides of a 30-60-90 triangle will always be in what ratio?
x:x*root3:2x
Where x is the length of the side opposite the 30 degree angle and x*root3 is the length of the slide opposite the 60 degree angle, and 2x represents the hypotenuse
What is the area of an equilateral triangle?
(S^2*root3)/4
Dropping an altitude from the upper vertex to the base of an equilateral triangle produces what?
2 identical 30-60-90 triangles
What are the 3 ways triangles can be similar?
1) the 3 angles of 1 triangle are the same measure of the three angles of another triangle
2) the three pairs of corresponding sides have lengths in the same ratio
3) an angle of one of the triangles is the same measure as an angle of another triangle and the sides surrounding these angles are in the same ratio
What is a quadrilateral?
A four sided polygon: square, rectangles, parallelograms, rhombuses, and trapezoids
All square are….
Rectangles
All rectangles are…
Parallelograms
What is the area of a parallelogram?
base x height (the height is always perpendicular to the base)
What is a rectangle and what is the area of a rectangle?
Any quadrilateral with 4 right angles / a rectangle is also a parallelogram so opposite sides are equal
Length x width
The exterior angles of any polygon sums to what?
360 (take only 1 exterior angle per vertex)
What is the longest chord in a circle?
The diameter of the circle
What is the area of a circle?
pi*r^2 or pi(d/2)^2
What is the circumference of a circle?
2pir or pi*d
What is important to know about circles inscribed in equilateral triangles?
Each point at which the circle touches the triangle is the midpoint of the side of the triangle
By drawing a segment from the centre of the circle to the base of the triangle, two 30-60-90 triangles are created
How do you calculate the diagonal of a square?
Root 2 * length of a side
When a square is inscribed in a circle, a diagonal of the square is also what?
The diameter of the circle
When a circle is inscribed in a square, what must be true?
The diameter of the circle has the same length as a side of the square
The area of an inscribed square will be smallest when what?
The vertices of that square are located at the midpoints of the respective edges of the circumscribed square. The area of such an inscribed square will be half of the area of the circumscribed square.
In a two circle system, what is the area of the outer ring?
Pi * (R1^2 - R2^2) where RI is the radius of the outer circle and R2 is the radius of the inner circle
What is the longest line segment that can be drawn within a rectangular solid?
d^2 = l^2 + w^2 + h^2
What is the longest line segment that can be drawn within a cube?
d=s*root3
What is the surface area of a cube?
6s^2
What is the surface area of a rectangular solid?
2(LW) + 2(LH) + 2 (HW)
How do you find the number of sides of a regular polygon when given the interior angle?
((n-2)180) / n = interior angle
Where n is the number of sides
What is the area of a 30-60-90 triangle?
(x^2*root3)/2
What is the perimeter of a 30-60-90 triangle?
x (3+root 3)
What is the volume of a right circular cylinder?
pir^2h
What is the surface area of a right circular cylinder?
2pir^2 + 2pir*h
