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ASVAB Knowledge > 8. Geometry > Flashcards

8. Geometry Flashcards

1
Q

What is geometry?

A

Geometry is the branch of mathematics that deals with the properties of shapes, lines, points, angles, and other such objects and the relationships among them.

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2
Q

What do you know about an arc of a circle?

A

Arcs of a circle and sizes of angles are measured in degrees and (not very often) in minutes or even seconds; 1 degree equals 60 minutes, and 1-minute equals 60 seconds.

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3
Q

What does a circle have?

A

A circle has 360 degrees, any arc that isn’t a complete circle measures less than 360 degrees.

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4
Q

What is a quadrilateral?

A

A quadrilateral (a shape with four sides, such as a square or rectangle) has angles that add up to 360 degrees.

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5
Q

Two dimensional shapes can only be measured with…

A

length and width.

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6
Q

Three-dimensional shapes have…

A

length, width, and height (depth).

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7
Q

What is the perimeter of a shape?

A

The perimeter of a shape is the distance around it (you can view it as the shape’s boundary), and its area is all the flat space within that boundary.

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8
Q

How can you calculate the perimeter of 2D objects?

A

The perimeter of 2D objects is always the sum of the length of all its sides (even a circle has a side, though just one), and its area is usually the object’s length times its width or something pretty similar.

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9
Q

How does an angle can be formed?

A

Angles are formed when two lines intersect (cross) at a point. You typically measure angles in degrees. The greater the number of degrees the wider the angle is.

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10
Q

How many degrees are within a straight line?

A

180 degrees

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11
Q

How many degrees are within a right angle?

A

exactly 90 degrees

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12
Q

How many degrees are within an acute angle?

A

An acute angle is more than 0 degrees but less than 90 degrees.

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13
Q

How many degrees are within an obtuse angle?

A

An obtuse angle is more than 90 degrees but less than 180 degrees.

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14
Q

How much does a reflex angle measure?

A

A reflex angle measures more than 180 degrees.

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15
Q

What are complementary angles?

A

Complementary angles are two angles that equal 90 degrees when added together.

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16
Q

What are supplementary angles?

A

Supplementary angles are two angles that equal 180 degrees when added together!

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17
Q

What are the 7 basic different types of angles?

A
  1. Straight lines
  2. Right angles
  3. Acute angles
  4. Obtuse angles
  5. Complementary angles
  6. Supplementary angles
  7. Reflexive angles
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18
Q

What are vertical angles?

A

Vertical angles oppose each other when two lines cross. They’re always equal. Angles 4 and 2 are equal, and angle 1 and 3 are equal. In this case, the term vertical refers to where the lines cross each other; it has nothing to do with direction.

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19
Q

What are parallel lines?

A

Parallel lines never intersect. Lines are considered parallel if they’re equidistant and they’ll never meet. They also point in the same direction.

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20
Q

What are corresponding angles?

A

Corresponding angles have the same measure. They’re on the same side of the transversal and both either above or below the parallel lines.

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21
Q

What is the term transversal means?

A

Transversal means a line that crosses through a parallel line.

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22
Q

What are alternate exterior angles?

A

Alternate exterior angles are on the opposite sides of the transversal and between the parallel lines. Equality between these angles means you have a parallel line on your hands.

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23
Q

What are consecutive interior angles?

A

Consecutive interior angles are on the same side of the transversal, between the parallel lines. If these two angles add up to 180 degrees, you’re dealing with parallel lines.

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24
Q

How do you name angles?

A

You can name angles by using the vertex point and a point on each of the angle’s ray. You may see problems where angles are named ∠ABC, you can also use the vertex only to name an angle e.g., ∠B

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25
Q

Define a triangle.

A

A triangle consists of three straight sides that intersect at the three vertices. Additionally, all three angles always add up to 180 degrees.

26
Q

What are the 5 different types of a triangle?

A
  1. Isosceles triangle
  2. Equilateral triangle
  3. Right triangle
  4. Obtuse triangle
  5. Scalene triangle
27
Q

What is an isosceles triangle?

A

An Isosceles triangle had two equal sides; the angles opposite the equal sides are also equal.

28
Q

What is an equilateral triangle?

A

An equilateral triangle has three equal sides; each of the angles measures 60 degrees.

29
Q

What is a right triangle?

A

A right triangle has one right angle 90 degree; therefore, the remaining two angle are complementary (add up to 90 degrees). The side opposite the right angle is called the hypotenuse, which is the longest side of a right triangle. the other two sides are called legs.

30
Q

What is an obtuse triangle?

A

An obtuse triangle has an angle greater than 90 degrees.

31
Q

What is a scalene triangle?

A

A scalene triangle has three unequal sides.

32
Q

How can you find the perimeter of a triangle?

A

You can find the perimeter of a triangle by adding together the lengths of the three sides.

33
Q

How can you calculate the area of a triangle?

A

A=½bh

The area of a triangle is equal to one-half of base (the bottom, or the length) and the height.

34
Q

What is the Pythagorean theorem? Explain.

A

The Pythagorean theorem only works with right-angles triangles. The formula for this theorem is a2+b2=c2, where a and b are the triangle’s legs and c are its longest side.

35
Q

What are quadrilaterals again?

A

Shapes with four sides — all contain angles totaling 360 degrees.

36
Q

What are squares.

A

Squares have four sides of equal length, and all the angles are right angles.

37
Q

What are rectangles?

A

Rectangles have all (four) right angles, and the opposite sides equal lengths.

38
Q

What are parallelograms?

A

Parallelograms have opposite sides that are parallel, and their opposite sides and angles are equal: angles don’t have to be right angles.

39
Q

What are rhombuses?

A

Rhombuses gave four sides of equal length, but the angles don’t have to be right angles.

40
Q

What are trapezoids?

A

Trapezoids have exactly two sides that are parallel.

41
Q

How can you find the area of a square and a rectangle?

A

You can find the area of a square and a rectangle with the formula A=lw, where A represents area, l represents length of one side, and w represents width.

42
Q

How can you find the area of a parallelogram?

A

You can find the area of a parallelogram with A = bh.

43
Q

How can you find the area of a rhombus?

A

You can find the area of a rhombus by using the equation A=pq/2, where A represents Area, p represents the length of a one diagonal, and q represents the length of the other diagonal.

44
Q

What is the formula to find the area of a trapezoid?

A

A = a+b/2 (h), where A represents area, a represents the length of one base (one of its parallel lines), and b represents the length of the other base (the other parallel line). In this formula, h represents height as measured between the two parallel lines.

45
Q

What is a circle?

A

A circle is formed when its points are all located an equal distance from its center. A circle always has 360 degrees.

46
Q

What is a circumference?

A

Circumference is the points forming the circle — that is, the distance around the circle.

47
Q

What is the radius of a circle?

A

The radius of a circle is the straight-line measurement from the center of the circle to any point on the circumference of the circle.

48
Q

What is the diameter of the circle?

A

The diameter of the circle is measured as a line passing through the center of the circle, from a point on one side of the circle all the way to a point on the other side of the circle. Any line that passes through a circle and connects two points on the circle is called a chord. The diameter is the longest chord.

49
Q

The diameter of a circle is always twice as long as the radius of a circle, express in these in a mathematical equation.

A

d = 2r

50
Q

What are the formulas for the circumference of a circle?

A

The formula of the circumference of a circle are:

C=2πr

C=πd

51
Q

What is the formula of the area of a circle?

A

A = πr2

52
Q

What is the formula for finding the volume of a rectangular prism?

A

V = lwh

53
Q

What is the formula used in order to find the volume of cylinders?

A

V = πr2h

[basically, (A=πr2) and multiply the area with the height.

54
Q

What is the formula used in order to find the volume of a sphere?

A

V = 4/3πr3

55
Q

What is a surface area?

A

A surface area is all the area on the exterior of a solid.

56
Q

What is the formula of the surface area of a cube?

A

SA = 6s2

s represents the length of the side of each edge.

57
Q

What is the formula for surface area of a rectangular prism?

A

SA = 2ab + 2bc + 2ac

where a, b, and c represent the lengths of the three sides.

58
Q

What is the formula for the surface area of any prism?

A

SA = 2B + ph

where B represents the area of the base, p represents the perimeter of the base, and h represents height.

59
Q

What is the formula for the surface area of a cylinder?

A

SA = 2πr2 + 2πrh

60
Q

What are nonstandard shapes?

A

A mashup of two or more shapes.

61
Q

What do you need to do if you encount3er a nonstandard shape as a problem in your ASVAB test?

A

Break them apart and perform multiple sets of calculations.

62
Q

What formula can represent a line on a coordinate grid?

A

the slope-intercept form of a linear equation:

y=mx+b

where m represents the line’s slope, b represents the point where the line crosses the y-axis, and x and y represent coordinates of points that lie on the line.

ASVAB Knowledge (21 decks)

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