| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.74 |
| Score | 0% | 55% |
If the length of AB equals the length of BD, point B __________ this line segment.
bisects |
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intersects |
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trisects |
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midpoints |
A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.
The dimensions of this trapezoid are a = 5, b = 3, c = 6, d = 3, and h = 4. What is the area?
| 24 | |
| 13\(\frac{1}{2}\) | |
| 16\(\frac{1}{2}\) | |
| 12 |
The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:
a = ½(b + d)(h)
a = ½(3 + 3)(4)
a = ½(6)(4)
a = ½(24) = \( \frac{24}{2} \)
a = 12
Order the following types of angle from least number of degrees to most number of degrees.
right, acute, obtuse |
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right, obtuse, acute |
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acute, right, obtuse |
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acute, obtuse, right |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.
If angle a = 62° and angle b = 35° what is the length of angle d?
| 143° | |
| 153° | |
| 140° | |
| 118° |
An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:
d° = b° + c°
To find angle c, remember that the sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 62° - 35° = 83°
So, d° = 35° + 83° = 118°
A shortcut to get this answer is to remember that angles around a line add up to 180°:
a° + d° = 180°
d° = 180° - a°
d° = 180° - 62° = 118°
Solve for b:
b2 - 13b + 48 = b - 1
| -2 or -5 | |
| 7 or 5 | |
| -4 or -5 | |
| 7 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
b2 - 13b + 48 = b - 1
b2 - 13b + 48 + 1 = b
b2 - 13b - b + 49 = 0
b2 - 14b + 49 = 0
Next, factor the quadratic equation:
b2 - 14b + 49 = 0
(b - 7)(b - 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, (b - 7) must equal zero:
If (b - 7) = 0, b must equal 7
So the solution is that b = 7