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geometery mod2, tC/D
similar triangles, geometric mean and theroms
| Question | Answer |
|---|---|
| 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 |
| similarity transformation | a transformation in which there is a composition of a dilation with one or more basic rigid motions |
| In similar triangles, angles are ___________ | congruent, because similarity transformations all preserve angles |
| 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 ------- AB |
| property of similar triangles | corresponding angles of similar triangles are congruent, corresponding sides of similar triangles are proportional |
| what are the three similarity criterias | AA postulate, SAS similarity theorem, SSS similarity theorem |
| in a proportion, the product of the means_______________ | is equal to the product of the extremes |
| altitude | a segment from a vertex drawn perpendicular to the opposite side. it is used to calculate the height of the figure |
| geometric mean | when two numbers, a and b, have a unique number x such that : a x --- = ---- x b |
| what is the rationalize the denominator rule | when you eliminate the radicals from in order to fully simplify the expression |
| orthocenter | the point of concurrency of the three altitudes of a triangle |
| 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. |
| how do you construct an orthocenter | draw the three altitudes of a triangle |
| Pythagorean theorem | a² + b² = c², when given a right triangle |
| When the altitude is drawn to the hypotenuse of a right triangle ___________ | three similar triangles are formed |
| what is the geometric mean altitude formula |
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