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Math
Geometry
Elem Math Exam 3
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Terms in this set (48)
Congruent
same size and same shape
What is a feature of congruent figures?
corresponding parts of the figures have exactly the same geometric measures
Can you have two figures that are the same shape but not the same size?
yes
Enlargements and reductions are also called what?
miniatures
What are two shapes that are related?
similar figures
What makes two shapes similar?
if the points of the two shapes can be matched so that every pair of corresponding angles have the same size
What is a scale factor?
the ratios from every pair of corresponding lengths all equal the same value
Formula for scale factor?
new length to old length
New length = ?
scale factor x corresponding old length
What are similar triangles?
they have the same shape but are just scaled differently; they have congruent angles and proportional sides
What is true about the angles of similar triangles?
they are congruent
What is true about the sides of similar triangles?
congruent sides of similar triangles are proportional
What is the similarity ratio (aka scale factor)?
The ratio between corresponding sides.
How do you find the similarity ratio?
Match up any pair of corresponding sides and set up the ratio
What three criteria hold if two triangles are said to be similar?
AAA criteria
SSS criteria
SAS criteria
Suppose the scale factor for the dilation of a figure is one. What will be true of the image?
The image would be the exact same
What symbol would be used to show two figures are similar?
~
AAA criteria
two triangles are similar if either all the three corresponding angles are equal or any two corresponding angles are equal
SSS Criteria
two triangles are said to be similar, if all the corresponding sides are in the same proportion
SAS Criteria
Two angles are similar if their two corresponding sides are in the same proportion and the corresponding angles between these sides are equal
What must be true of a circle has a circumference of Pi?
the diameter is Pi, too
How does one obtain Pi?
circumference over diameter
If the diameter of a circle is 12, what is the length of the radius?
6
What is another name for the original figure we are dealing with similar figure?
Pre image
What is unique about tangent lines?
its a line that only touches the circle on one point
central angle
an angle that is within the shape on the center of the circle
central angle of circle
inscribed angle
-An angle with its vertex on the circle and its sides along chords of the circle
-intercepts at arc
inscribed angle in circle
Perpendicular bisector
bisects a line segment into two equal parts; the bisector marks the midpoint of the line
perpendicular bisector of circle
Two or more circles with the same center are called what?
Concentric circles
What is it when an angle with its vertex at the center of the circle cuts a piece of the circle?
Arc
What is "part of the circumference" called?
arc
examples of similar figures
squares, circles, cubes
What are the two main "slices" of a circle?
sector
segment
If the diameter of a circle is 9, does every chord of the circle equal 9?
no, because the chord is not always located directly in the middle of the circle where the diameter is measured.Therefore, the chord will vary in measure
Angle bisector
one angle is cut into two angles of the same size
Tangent
a line that touches a circle in only one point
Sphere
the 3D set of points at a fixed distance from a fixed point
hemisphere
half a sphere
volume of similar polygons
Scale factor cubed
area of similar polygons
Scale factor squared
Perimeter of similar polygons
scale factor
What is a way of getting similar polygons?
size changes or size transformation
arbitrary
Which ever shape is new or old
Congruent figures
corresponding parts of the figure, has exactly the same geometric measures
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