similar triangles, geometric mean and theroms
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| similarity in figures | two figures are similar if and only if one can be obtained from the other by a single or sequence of basic rigid motions and a dilation
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| similarity transformation | a transformation in which there is a composition of a dilation with one or more basic rigid motions
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| In similar triangles, angles are ___________ | congruent, because similarity transformations all preserve angles
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| in similar triangles, sides are ___________ | proportional, because DE= AB * k, EF= BC*k & DF= AC * k where k is the scale factor between triangle ABC and triangle DEF, k = DE
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AB
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| property of similar triangles | corresponding angles of similar triangles are congruent, corresponding sides of similar triangles are proportional
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| what are the three similarity criterias | AA postulate, SAS similarity theorem, SSS similarity theorem
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| in a proportion, the product of the means_______________ | is equal to the product of the extremes
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| altitude | a segment from a vertex drawn perpendicular to the opposite side. it is used to calculate the height of the figure
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| geometric mean | when two numbers, a and b, have a unique number x such that :
a x
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x b
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| what is the rationalize the denominator rule | when you eliminate the radicals from in order to fully simplify the expression
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| orthocenter | the point of concurrency of the three altitudes of a triangle
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| how do you construct an altitude | 1) Draw triangle ABC.
2) Place compass on point 𝐴
3) Draw an arc that crosses line 𝐵𝐶 at two points. Label them
D and E.
4) With the compass on point D, draw an arc below line
BC.
5) Do the same from point E (same compass width), making the arcs cross. Label the crossing point F.
6) Draw a straight line from A through point
F.
This line is the altitude — it's perpendicular to
BC.
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| how do you construct an orthocenter | draw the three altitudes of a triangle
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| Pythagorean theorem | a² + b² = c², when given a right triangle
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| When the altitude is drawn to the hypotenuse of a right triangle ___________ | three similar triangles are formed
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| what is the geometric mean altitude formula |
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