Two figures whose sides are proportional and angles are congruent
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What are the three properties used to determine similar triangles?
SSS proportion theorem, SAS proportion theorem, and AA congruence theorem
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Where do the first and second numbers in ratio notation go in a fraction?
The first number is the numerator and the second number is the denominator
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What is a proportion?
An equation stating that two ratios are equal
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What are the extremes in a proportion?
The numerator of the first ratio and the denominator of the second
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What are the means in a proportion?
The denominator of the first ratio and the numerator of the second
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What is a cross-product?
The product of the means and the product of the extremes
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Describe the cross product property.
In a true proportion, the product of the means is equal to the product of the extremes
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The perimeters of similar polygons are what?
proportional!
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What specific triangle is always similar to other triangles of its type?
A right isosceles triangle
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What is an arithmetic sequence?
A pattern where the next number in the sequence is determined by adding or subtracting the previous number by a constant called a scale factor
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What is a geometric sequence?
A pattern where the next number in the sequence is determined by multiplying the previous number by a constant called a scale factor
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Consecutive terms of a geometric sequence are what?
proportional!
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What is a geometric mean?
The term between any two numbers in a sequence. If this number is unknown, the equation is written as a/x=x/b
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What is an altitude?
A segment drawn from a vertex of a triangle perpendicular to the opposite side.
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Describe the right triangle similarity theorem:
If the altitude of a right triangle is drawn to its hypotenuse, then the new triangles formed are similar to each other and the original triangle
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Describe the heartbeat theorem:
The length of the altitude in a right triangle is the geometric mean of the two segments created by the altitude and the hypotenuse
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Describe the boomerang theorem:
The length of an included leg of two similar right triangles is the geometric mean of the hypotenuse that is adjacent of that leg
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Describe the side-splitter theorem:
If a line is parallel (like a transversal) to one side of a triangle and intersects the other two sides, then it divides those sides proportionally
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Describe the triangle-angle-bisector theorem:
If a segment bisects an angle of a triangle, then it divides the opposite side into two segments whose ratio is proportional to the ratio other two sides of the triangle