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79 Cards in this Set
- Front
- Back
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Define Acute Angle
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mesures less than 90 d
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Define obtuse angle (more than but less than?)
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more than 90d but less than 180d
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Define Straight angle
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180d
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What is the sum of two or more angles that form a straight line?
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180d
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What are vertical angels?
Vertical measures have __ measures? |
When two lines intersect, four angels are formed. The two angles in each pair of opposite angles are vertical angels.
They have equal measures |
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What are perpendicular angels?
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Four lines that intersect, all four right angels.
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What does bisect mean?
What is a midpoint? |
A line that "cuts through" another one.
The midpoint is at the cross-section. |
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What is a transversal?
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If a third intersects a pair of parallel, eight angles are formed.
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What will the eight angles be if a pair of lines are cut by a transversal that is perpindicular to the parallel lines?
Not perpendicular? |
Right angles
Four of the angles are acute and four obtuse; four of the acute angles are equal four of the obtuse angels are equal |
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What is the sum of any acute angel and any obtuse?
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180d
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If a pair of lines that are not parallel is cut by a transversal, then what properties do not apply?
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See page 473
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What is the sum of all 3 angels in a triangle?
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180d
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What is an exterior angel?
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When angels like <BCD are formed by one side of a triangle ABC and the extension of another side
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In any triangle:
The longest side is? The shortest side is opposite? The sides with the same length are opposite angles with? |
opposite the largest angle
opposite the smallest angle the same measure |
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Define scalene
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3 different lengths
3 different angles |
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Define isosceles
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2 lengths the same
2 angles the same |
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Define equilateral
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all 3 lengths the same
all 3 angles the same |
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Define hypotenuse
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Side opposite a 90d angle
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What are "legs"?
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The two sides that are not the hypotenuse
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In any right angle triangle, what is the sum of the measures of two acute angels?
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90d
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What is the pythagorean theorem?
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In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can be written as an equation: where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. |
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When is it true that
a2 + b2 = c2? a2 + b2 = < c2? a2 + b2 = >2? |
<ABC pg 480
If angle C is a right angle If angle C is obtuse Ir angle C is acute |
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Can you remember the most common right triangles?
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3, 4, 5
3x, 4x, 5x 5, 12, 13 x,x,x,SR12 s,s,SR2, 2x |
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For any positive number x, there is a right angle whose sides are?
What if x is not an integer? |
3x, 4x, 5x
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In a 45-45-90 Right triangle, how can you get the hypotenuse?
Length of each leg? |
In a right triangle the sides are x, x, and xSR2 so by multiplying the length of a leg by SR2 you get the hypotenuse.
For length of each leg, divide by SR2 |
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What does the diagonal of a square divide into?
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It divides the square into two isosceles right triangles.
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What does an altitude divide an equilateral into?
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two 30-60-90 right triangles.
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In a 30-60-90 Right triangle the sides are?
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x,x,SR3 and 2x
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If you know the length of the shortest leg, how do you find the longer leg? Hypotenuse?
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Multiply it by SR3 to get longer leg
Multiply it by 2 to get hypotenuse. |
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If you know the length of the longer leg, how do you find the shorter leg? Hypotenuse?
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Divide it by SR3 to get shorter leg
Multiply shorter leg by 2 to get hypotenuse |
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If you know the length of the hypotenuse, how do you get the shorter leg? Longer leg?
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Divide it by 2 to get shorter leg
Multiply shorter leg by SR3 to get longer leg. |
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What is meant by triangle inquality?
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the sum of the lengths of any two sides of a triangles is greater than the length of the third side
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What is the difference of the lengths of any 2 sides of a triangle?
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It is less than the length of the third side.
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What is the formula for the area of a triangle?
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A = 1 over 2 by bh
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In a right triangle, what can be the base and height?
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either leg.
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If A represent the area of an equliateral triangle with side S, then A = ?
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A = s squared SR3 over 4
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Define polygon
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closed geometric figure made up of line segments
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What are vertex's vertices?
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endpoints of the sides/ lines
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What is a diagonal?
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A line inside a polygon drawn from one vertex to another
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What is the smallest polygon? What is a quadrilateral? Pentagon? Hexagon? Octagon? Decagon?
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Triangle
Four sides; five, six, eight and ten sides |
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Every quadrilateral has how many diagonals?
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two
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The sum of the measures of the n angles in a polygon with n sides is?
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(n-2) * 180d
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In any quadrilateral, the sum of the measures of the four angles is?
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360d
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In any polyogn, the sum of the exterior anhle, taking one at each vertex is what?
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360d
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What is a regular polygon?
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all of the sides are the same length and each angle has the same measure
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In an y regular polygon, the meaurre of each interior angle is what?
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(n-2) * 180d over n and the measure of each exterior angle is 360d over n
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Define parrallelogram
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a quadrilateral in which both pairs of opposite sides are parallel
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Re Parrallelogram:
opposite sides are? opposite angles are? Consecutive angles add up to? 2 diagonals bisect? A diagonal divides what? Into? |
Equal: AB = CD and AD = BC
equal: a = c and c = d 180d: a + b = 180 b + c = 180 c + d = 180 and a + d = 180 The two diagonals bisect each other AE = EC and BE = ED Two triangles that have the exact size and shape (the triangles are congruent) |
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Define rectangle
The measure of each angle in a rectangle is? Diagonals of a rectangle have? |
Parrallelogram in which all four sides are right angles
90d The same length AC = BD |
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What is a square?
Each diagonal divides the square into? The diagonals are perpendicular to? |
A rectangle, but all four sides have the same length
two 45-45-90 right triangles To each other |
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What is a trapezoid?
What are the bases? Are they ever equal? Are the nonparallel sides ever equal? |
A quadrilateral in which one pair of sides is parallel and the other pair of sides are not.
the parallel sides are called bases. Bases are never equal. nonparallel sides are not usually equal but if they are it is called an isosceles trapezoid. |
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What is the area formula for a parallelogram?
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A = bh
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What is the area formula for a rectangle?
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A = lw
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What is the area formula for a square?
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A = s to the power of 2
or A = 1 over 2 (d to the power of two) |
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What is the area formula for a trapezoid?
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A = 1 over 2 (b1 + b2)h
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Do 2 rectangles with the same perimeters have the same area? Vise versa?
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They can both be different.
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For a given perimeter, the rectables iwth the __ area is a __?
For a given area the rectangle with the __ perimeter is a __? |
Largest; square
smallest; square |
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Define radius
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adius: 1/2 of a circle's diameter, it's a line segment that connects the center with a point on the circle
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define: central angle of a circle
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central angle: an angle formed by two radai
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define: circumference
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circumference: the distance around a circle = (2)(pi)(r)
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define: arc length
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arcs are the portion of a circle cut off by a particular central angle. The degree measure of an arc is equal to the central angle that cuts it off
arc length = n/360 x (2)(pi)(r) |
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area of a circle
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area of a circle = (pi)(r^2)
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Any triangles, formed by coneccting the endpoints of two radii, is what?
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An isosceles
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What is the degree measure of a complete circle?
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360d
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The degree measure of an arc equals the degree measure of what?
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The central angles that intercepts it.
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If an arc measures x, what is the length of the arc?
The area of the sector is formed by what? |
x over 360d (2pier)
the arc and 2 radii is x over 360 (piersquared) |
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What is a line and a circle or two circles tangent?
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If they have only one point of intersection
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When is a circle inscribed in a triangle or square?
When is a polygon inscribed in a circle? |
If is is tangent to each side
If each vertex is on the circle. |
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If a line is tangent to a circle, a radius (or diameter) drawn to the point where the tangent touches the circle is what?
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perpendicular to the tangent line.
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What units is volume in?
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Cubic units
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What is the formula for the volume of a rectangle?
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V = lwh
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What is the formula for the voume of a cube?
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V = e*e*e = e to the power of 3
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Define surface area for a rectangle
For a cube? |
Rect: A = 2(lw+lw+wh)
Cube: A = 6e to the power of 2 |
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What is the longest lie segment that can be drawn between two points on a box?
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The diagonal
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If the dimensions of a box are l,w,and h, and is d is the length of the diagonal, then what is dsquared?
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dsquared = lsq + wsq + hsq
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What is the volume of a cylinder?
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Area of it's circular base (so, pie r sq) times its height.
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The formula for the volume of a cylinder whose circular base has a radius of r and the height is h is what?
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V = (piersquared)(h)
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The surface area of the side of a cylinder is the circumference of the circular base times the height is what?
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A = (2piersquared)(r)(h)
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The area of the top and bottom are each piersquared, so that is the total of a can?
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2piersquared(r)(h) + 2piersquared
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