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What is a similar (~) shape?
Two figures whose sides are proportional and angles are congruent
What are the three properties used to determine similar triangles?
SSS proportion theorem, SAS proportion theorem, and AA congruence theorem
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
What is a proportion?
An equation stating that two ratios are equal
What are the extremes in a proportion?
The numerator of the first ratio and the denominator of the second
What are the means in a proportion?
The denominator of the first ratio and the numerator of the second
What is a cross-product?
The product of the means and the product of the extremes
Describe the cross product property.
In a true proportion, the product of the means is equal to the product of the extremes
The perimeters of similar polygons are what?
proportional!
What specific triangle is always similar to other triangles of its type?
A right isosceles triangle
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
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
Consecutive terms of a geometric sequence are what?
proportional!
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
What is an altitude?
A segment drawn from a vertex of a triangle perpendicular to the opposite side.
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
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
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
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
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
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