Chapter 6 Flashcards
Converse of Side Splitter Theorem
If a line divides two sides of a triangle proportionally, then it is parallel to the 3rd side.
Side Splitter Theorem
If a line is parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
Extension of Side Splitter Theorem
If 3 parallel lines intersect two transversal, then they divide the transversals.
Angle Bisector Theorem
If a ray bisects an angle of a triangle, then it divides the opposite sides into segments proportional to their adjacent side.
SSS Similarity Theorem
If the ratios of 3 pairs of corresponding sides are equal, then the triangles are similar.
SAS Similarity Theorem
If the ratios of 2 pairs of corresponding sides are equal, and the included angles are congruent,then the triangles are similar.
AA Similarity Postulate
If two sets of corresponding angles of triangles are congruent, then the triangles are similar (shortcut: 2 angles are congruent, 3rd angle is automatically congruent by third angle theorem.)
Congruent Polygons Have….
Same size and same shape
Similar Polygons…
Corresponding angles are congruent
Corresponding side lengths are in the same proportion
Same shape,but can be different size
Ratio
Comparison of Two Numbers Using Division
Extended ratio
More than two numbers in a ratio
Proportions
2 or more ratios in an equation
Scale factor
The ratios of the lengths of two corresponding sides
Written as fully reduced ratio or fraction
No units
SSS Similarity Theorem
If two ratios of 3 pairs of corresponding sides are equal, then the triangles are similar
SAS Similarity Theorem
If two ratios of 2 pairs of corresponding sides are equal, and the included angles are congruent, then the triangles are similar
