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Chapter 7- Geometry
| Question | Answer |
|---|---|
| ratio | comparison of two quantities using division |
| extended ratios | used to compare three of more quantities |
| proportion | an equation stating that two ratios are equal |
| extremes | a/b = c/d; a and d |
| means | a/b = c/d; b and c |
| cross products | the product of the extremes and and the means |
| cross products property | in a proportion, the product of the extremes equals the products of the means |
| equivalent proportions | as long as the original extremes and original means are cross products, the proportion is equivalent |
| similar polygons | two polygons are similar if and only if their corresponding angles are congruent and corresponding side lengths are proportional |
| perimeters of similar polygons | if two polygons are similar, then their perimeters are proportional to the scale factor between them |
| scale factor | the ratio of the lengths of the corresponding sides of two similar polygons |
| angle-angle similarity | if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar |
| side-side-side similarity | if the corresponding side lengths of two triangles are proportional, then the triangles are similar |
| side-angle-side similarity | if the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle, and the included angles are congruent, then the triangles are similar = |
| triangle proportionality theorem | if a line is parallel to one side of a triangle and intersects the two other sides, then it divides the sides into segments of proportional lengths. |
| converse of triangle proportionality theorem | if a line intersects two sides of a triangle and separates the sides into proportional corresponding segments, the the line is parallel to the third side of the triangle |
| mid segment of a triangle | a segment with endpoints that are the midpoints of two sides of the triangle |
| triangle mid segment theorem | a mid segment of a triangle is parallel to one side of the triangle and its length is one half the length of that side |
| proportional parts of parallel lines | if three or more parallel lines intersect two transversals, then they cut off the transversals proportionality. |
| congruent parts of parallel lines | if three or more parallel lines cut off congruent segments on one transversal, they they cut off congruent segments on every transversal |
| altitudes of similar triangles | if two triangles are similar, the lengths of the corresponding altitudes are proportional to the lengths of the corresponding sides |
| angle bisectors of similar triangles | if two triangles are similar, the lengths of the corresponding angle bisectors are proportional to the lengths of corresponding sides |
| medians of similar triangles | if two triangles are similar, the lengths of corresponding medians are proportional to the lengths of corresponding sides |
| triangle angle bisector | an angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two segments. |
| dilation | a transformation that enlarges or reduces the original figure proportionally |
| similarity transformaiton | when a dilation produces a similar figure |
| center of dilation | a fixed point that dilations are performed around |
| scale factor of a dilation | describes the extent of the dilation; ratio of a length on the image to a corresponding length on the preimage |
| two types if dilations | enlargement and reduction |
| enlargement | a dilation with a scale factor greater than 1, or an image that is larger than the original figure |
| reduction | a dilation with a scale factor less than 1, or an image that is smaller than the original figure |
| scale model/scale drawing | an object or drawing with lengths proportional to the object it represents |
| scale | ratio of a length on the model or drawing to the actual length of the object being modeled or drawn |
Created by:
Maxbf2001