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Geometry Chapter 7
| Term | Definition |
|---|---|
| ratio | a comparison between 2 quantities; always have the same units; written 3 ways; SIMPLIFY!! |
| always change the bigger unit | to the smaller |
| extended ratio | compare 3 or more quantities |
| proportion | 2 equal ratios |
| a:b=c:d | a & d are extremes, b & c are means |
| similar polygons have | congruent corresponding angles, proportional corresponding sides, the common proportion is called the scale factor |
| angles in similar polygons | don't use the scale factor, they remain the same |
| the ratio of perimeters is | congruent to the scale factor |
| AA | if 2 angles of one triangle are congruent to 2 angles of a second triangle, the triangles are similar |
| SSS~ | if the measures of corresponding sides of 2 triangles are proportional, the triangles are similar (same scale factor) |
| SAS~ | if the measures of 2 sides of a triangle are proportional to the corresponding sides of another triangle and the included angles are congruent, the triangles are similar |
| CSSTP | corresponding sides of similar triangles are proportional |
| to verify the midsegment theorem | 1. find midpoint of sides to make midsegment (midpt formula) 2. make sure the distance of midsegment drawn is half of the base (distance formula) 3. make sure midsegment and base are parallel (slope formula) |
| the midsegment is | 1/2 of the base |
| triangle proportionality theorem | if a line is parallel to one side of a triangle and intersects the other two sides NOT as a midpoint, then it separates the sides into proportional lengths |
| triangle midsegment theorem | if a midsegment joins two midpoints of sides of a triangle, then that segment is parallel to the third side |
| if 3 or more parallel lines intersect 2 transversals | then they cut off the transversals proportionally |
| if 3 or more parallel lines cut off congruent segments on 1 transversal | then they cut off congruent segments on every transversal |
| altitude | segment that connects an angle of a triangle perpendicular to the opposite side |
| if 2 triangles are similar | then the lengths of the corresponding altitudes have the same ratio as the scale factor |
| if 2 triangles are similar then | the lengths of the angle bisectors have the same ratio as the sale factor |
| an angle bisector of a triangle separates the opposite side into | 2 segments that are proportional to the lengths of the other 2 sides |
| median | connects an angle to the midpoint of the opposite side |
| if two triangles are similar, the lengths of the corresponding medians are | proportional to the lengths of corresponding sides |
Created by:
ts2819
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