Math Test 3
What is the circumference divided by the diameter of any circle?
Pi
What is the formula for the circumference of a circle?
Pi x the diameter OR (2)Pi x radius
What is the distance from the center of circle to any point on it?
Radius
Congruent
Same size and same shape
What is the amount by which the image grows or shrinks called?
Scale Factor
What is like a slice of pie (a circle wedge)?
Sector
What is the difference between similarity and congruency?
Similar figures have same shape, whereas congruent figures have same shape AND size.
What are similar triangles?
Similar triangles have the same shape but are just scaled differently. Similar triangles have congruent angles and proportional sides
What is a line perpendicular to the radius that touches ONLY one point on the circle?
The tangent of the circle
What is the center of the circle?
Origin
Always True, Sometimes True, Never True: A radius of a circle can have both endpoints on the circle.
Never True
An angle with its vertex at the center of the circle is what?
A central angle of the circle
When drawing a squiggly line on paper, you have drawn a what?
A curve
How do you get the scale factor?
New length to Old length
A diameter of a circle is a chord of the circle?
Always True
A radius of a circle has a length that is half the length of a diameter of the circle?
Always True
The bisector of an angle is a line of symmetry for the angle?
Always True
The distance between the center of a circle and a point on the circle is the same as the length of a radius?
Always True
The perpendicular bisector of a line segment is a line of symmetry fro the line segment?
Always True
Two circles with the same length for radius are exactly the same size?
Always True
What are the criteria for two triangles to be similar?
Angle, Angle, Angle (all angles are = to corresponding) Angle, Angle (at least 2 are b/c other one will be) Side, Side, Side (sides are proportional to corresponding) Side, Angle, Side (two sides are proportional and angle is equal)
What is a curved line that is part of circumference of a circle
Arc
What is a line segment within a circle that touches 2 points on the circle?
Chord
What is the distance around the circle?
Circumference
What is a feature of congruent figures?
Corresponding parts of the figures have exactly the same geometric measures
What is true about the sides of similar triangles?
Corresponding sides of similar triangles are proportional
What is the longest distance from one end of a circle to the other?
Diameter
What is the transformed figure called?
Dilated Image
How can two shapes be similar?
If the two shapes can be match so that: every pair of corresponding angles have the same size AND the ratios from every pair of corresponding lengths all equal the same value called the scale factor
An angle with its vertex on the circle and its sides along chords of the circle is called a what?
Inscribed angle
What if something has a scale factor of 1?
It is the original image
What if something has a negative scaled factor?
It would be the opposite direction (-2 x 1 = -2)
What is another word for reductions?
Miniatures
What does not matter for similar figures?
Size
A chord of a circle is a diameter of the circle?
Sometimes True
Enlargements and reductions have what?
The exact same shape as the original shape
What if the scale factor is 0?
Then the image would be 1 single point
What is true about the angles of similar triangles?
They are congruent
True or False: Every diameter is also a chord?
True
Definition of Similarity
Two geometrical figures are known as similar figures, if either both the objects have the same shape or one possesses same shape as the mirror image of another. We can say that if two images are similar, then by shrinking or enlarging one image, other can be obtained
What is a dilation?
Where the polygon grows or shrinks but keeps the same overall shape. It's like zooming in or out on a camera.
For two triangles to be similar...
all corresponding angles are equal and all corresponding sides are proportional
If one angle is cut into two angles of the same size, there is an ____________________
angle bisector
Old and New lengths are
arbitrary
What is the formula for the area of the circle?
area = Pi(r^2)
Two or more circles with the same center are said to be ___________
concentric circles
Multiplicative Comparisons are of _______________ ______________
corresponding lengths
Two figures that have the same shape but not the same size are said to be ___________________ _______________
geometrically similar
A _____________ is a half a sphere
hemisphere
A ______________ bisects a line segment into two equal parts.
perpendicular bisector
A __________ is the 3D set of points at a fixed distance from a fixed point. What is the fixed point called?
sphere, center
What are examples of curves in space?
springs and slinky toys
A line that touches a circle in only one point is called a _________ to the circle.
tangent
Two figures are said to be similar if...
the dimensions of two geometrical figures are different, but their shapes are exactly the same
We denote similarity by the symbol called...
the tilde ~
