Part 3: Geometry Flashcards
What is the equation to calculate the number of degrees in a polygon?
degrees = (n+2)*180, where n is the number of sides.
What is the pythagorean theorem?
a^2 + b^2 = c^2, used to determine length of sides in a triangle with one right angle (a right triangle).
What is an equilateral triangle?
a triangle where all three sides are the same length (congruent).
What is an isosceles triangle?
a triangle where two sides are congruent.
What are the ratio of sides in an isosceles right triangle?
a to a√2
What are the ratio of sides in an 30-60-90 triangle?
2a to a√3 to a
What is the area of a triangle?
(bh)/2, which is base times height divided by 2.
What makes for congruent triangles?
All sides are the same. Or one side and two angels are the same. Or one angle and two sides are the same.
What makes for similar triangles?
All three angles are the same.
What is the area of a quadrilateral?
A = bh
What is the area of a trapezoid?
A = 1/2(b1 + b2)h
In a circle, what is a chord?
A line segment whose end points touch a circle’s circumference.
How to determine the length of an arc?
Given the angle of the arc, the length of the arc can be calculated with the following ratio:
arc angle/360 = arc length/circumference
What is the area of a circle?
πr^2
What is the area of a sector?
Given the angle of the arc of the sector, the area can be calculated using the following ratio:
area of sector/area of circle = sector angle/360
What is special about an inscribed triangle and it’s angle (or side)?
If one of the sides is the diameter of the circle, then it is a right triangle. If one of the angles of an inscribed triangle is 90 degrees, than one of its sides if the diameter.
How is a polygon circumscribe a circle?
If all sides of the polygon are tangential, then it circumscribes the circle.
What are concentric circles?
Circles that share the same center point.
what is the volume of a rectangular solid?
V = lwh
What is the surface area of a rectangular solid?
A = 2(lw + wh + hl)
What is the a circular cylinder?
Is a can but where the circles can be slid on their respective planes in any direction.
What is a right circular cylinder.
A can.
What is an axis in a circular cylinder?
It is the line connecting the center of both circles in a cylinder.
What is the volume of a can?
V = πr^2h
What is the surface area of a can?
A = 2πr^2 + 2πrh
Given two parallel lines and two intersecting lines, one of the angles is 57 degrees and the other is 42. What are x and y.
x is also 57 degrees. y is 180-42, which is 138 degrees.
Given an isosceles triangle, and an outside angle of 125 degrees, what are x and y?
y is 125 degrees. x is 180 - 55 - 55 = 70 degrees.
Given two inside angles x and y and one outside angle z, what is their relationship to each other?
x + y = z
What is the sum of the interior angles inside a decagon?
8*180 = 1440 degrees
What is a single angle inside of a regular decagon?
144 degrees
The lengths of two sides of an isosceles triangle are 15 and 22. What are the possible values of the perimeter?
Perimeter could be 52 or 59.
Triangles PQR and XYZ are similar. If PQ = 6, PR = 4, and XY = 9, what is the length of side XZ ?
4/6 = x/9 = 6
What are the lengths of sides NO and OP of triangle NOP in Geometry Figure 34 below?
NO = 30, OP = √3400
smaller triangle has a area of 42. What is the area of a similar right triangle with a hypotenuse 3 times longer?
42 * 9 = 378
Exercise 10
Area of rectangle: 50
Area of triangle: 17.5
Length of diagonal: √125
Perimeter of rectangle: 30
Exercise 11. In Geometry Figure 37 below, ABCD is a parallelogram. Find the following.
(a) The area of ABCD
(b) The perimeter of ABCD
(c) The length of diagonal BD
Area: 48
Perimeter: 24 + 4√5
Length of diagonal: √116
Exercise 12. In Geometry Figure 38 below, the circle with center O has radius 4. Find the following.
(a) The circumference of the circle
(b) The length of arc ABC
(c) The area of the shaded region
Circumference: 8π
Length of arc: 8/9 π
Area of arc: 16/9 π
Exercise 13. Geometry Figure 39 below shows two concentric circles, each with center O. Given that the larger circle has radius 12 and the smaller circle has radius 7, find the following.
(a) The circumference of the larger circle
(b) The area of the smaller circle
(c) The area of the shaded region
Circumference: 24π
Area of smaller: 49π
Area of shaded: 144π - 49π = 95π
Exercise 14. For the rectangular solid in Geometry Figure 40 below, find the following.
(a) The surface area of the solid
(b) The length of diagonal AB
Area = 14 + 20 + 70 all times 2 = 208
Length of diagonal: √153
