Questions and Answers
If two polygons are similar, then their corresponding angles are __________________ and in _______________.
Congruent, proportion
Scale factor is the _________ of any two corresponding sides between similar polygons.
ratio
If two polygons are similar, then their _________ are proportional to the scale factor between them.
perimeters
What does the equation ad=bc represent?
Signup and view all the answers
What does the equation ba=dc represent?
Signup and view all the answers
What does the equation ac=bd represent?
Signup and view all the answers
What does the equation a+b/b = c+d/d represent?
Signup and view all the answers
If two ______ of one triangle are congruent to two angles of a second triangle, then the two triangles are similar.
Signup and view all the answers
SSS Similarity Theorem - If the corresponding side lengths of two triangles are ___________, then the triangles are similar.
Signup and view all the answers
SAS Similarity Theorem - If one angle of a triangle is ____________ to one angle of 2nd triangle, and the sides including those angles are in proportion, then the triangles are similar.
Signup and view all the answers
Triangle Proportionality Theorem - If a line is _________ to one side of a triangle and intersects the other two sides of the triangle, then it divides those sides _______________.
Signup and view all the answers
A line that contains the ____________ of one side of a triangle and is ____________ to another side, passes through the ___________ of the 3rd side.
Signup and view all the answers
Triangle Midsegment Theorem - The segment that joins the ________________ of two sides of a triangle is:
Signup and view all the answers
Proportional Parts of Parallel Lines - If _________ or more parallel lines intersect two ______________, then they divide the transversals proportionally.
Signup and view all the answers
Congruent Parts of Parallel Lines - If three or more parallel lines cut off congruent segments on ______ transversal, then they cut off congruent segments on __________ every transversal.
Signup and view all the answers
Triangle Angle Bisector Theorem - The bisector of an angle cuts its _________________ side into two parts that are proportional to the other two sides.
Signup and view all the answers
Study Notes
Similar Polygons
- Two similar polygons have congruent corresponding angles.
- The corresponding sides of similar polygons are in proportion, defined by the scale factor.
Scale Factor and Proportionality
- The scale factor is the ratio of any two corresponding side lengths between similar polygons.
- The perimeters of similar polygons are also proportional to the scale factor.
Triangle Similarity Theorems
- SSS Similarity Theorem: If the corresponding side lengths of two triangles are proportional, then the triangles are similar.
- SAS Similarity Theorem: If one angle of a triangle is congruent to one angle of a second triangle, and the sides including those angles are in proportion, then the triangles are similar.
Instruction on Triangle Proportionality
- Triangle Proportionality Theorem: A line parallel to one side of a triangle that intersects the other two sides divides them proportionally.
- A line containing the midpoint of one side and parallel to another side will pass through the midpoint of the third side.
Triangle Midsegment Theorem
- A segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.
Properties of Parallel Lines
- If three or more parallel lines intersect two transversals, they divide the transversals proportionally.
- If parallel lines cut off congruent segments on one transversal, they will cut off congruent segments on every transversal.
Triangle Angle Bisector Theorem
- The angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Challenge yourself with these flashcards covering key concepts from Chapter 7 of Geometry B. Learn about similar polygons, scale factors, congruency, and proportional relationships with engaging questions. Perfect for reinforcing your understanding before the test!
