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# Geometry Chapter 7

TermDefinition
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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