Unit 9: Similarity Geometry
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2 polygons are similar if…?
1) all pairs of CORRESPONDING ANGLES are congruent 2) the ratios of the LENGTHS of ALL pairs of CORRESPONDING SIDES are equal
why are 2 triangles congruent if they are similar?
their sides, altitudes, and angle bisectors are the same ratio
which aspects of similar figures are all in the same ratio?
corresponding SIDES, MEDIANS, ALTITUDES, DIAGONALS, ANGLE BISECTORS (Perimeter is also same ratio of the sides)
Area and Volume ratio of similar figures
Area- squared Volume- cubed
What is the similarity ratio?
The ratio of lengths of CORRESPONDING SIDES
Properties of the midsegment OF A TRIANGLE
1) the midsegment of a triangle is parallel to the THIRD SIDE of the triangle 2) 1/2 length of the third side of the triangle
Properties of the midsegment OF A TRAPEZOID
1) Parallel to the BASES of the trapzoid (top and bottom most frequently) 2) 1/2 SUM OF THE LENGTH OF BOTH BASES ADDED TOGETHER
Side-Splitter Theorem
If a line is II to one side of the triangle and intersects the other two sides, the sides are divided proportionally (proportions can be created based on line segments within the polygon)
Corollary Theorem
If THREE II LINES INTERSECT TWO TRANSVERSALS, the segments on the transversals are proportional
AA similarity theorem
If 2 angles of one triangle are congruent to two angles of another triangle, the triangles are similar
SSS similarity theorem
If 3 sets of corresponding sides for 2 triangles are in proportion to each other, the triangles are similar
SAS similarity theorem
If an angle of one triangle is congruent to the corresponding angle of another triangle and then lengths of the sides (including these angles) are in proportion, the triangles are similar
Cross Product Property
The product of the means is equal to the product of the extremes