Download Ch 7 Study Guide and Problems.pages

Geometry
Chapter 7 Study Guide (7.1-7.6) - Similarity
Vocabulary
ratio - compares two numbers by division
proportion - an equation stating two ratios are equal
similar polygons - two polygons with congruent corresponding angles and
proportional side lengths
similarity ratio - the ratio of the corresponding sides of two similar polygons
dilation - a transformation that changes the size of a figure but not its shape
scale factor - describes how much the figure is enlarged or reduced
Theorems, Postulates, and Properties
Angle-Angle Similarity Postulate (AA~) - If two angles of one triangle
are congruent to two angles of another triangle, then the triangles are
similar.
Side-Side-Side Similarity Theorem (SSS~) - If the three sides of one
triangle are proportional to the three corresponding sides of another
triangle, then the triangles are similar.
Side-Angle-Side Similarity Theorem (SAS~) - If two sides of one
triangle are proportional to two sides of another triangle and their
included angles are congruent, then the triangles are similar.
• Triangle Proportionality Theorem - If a line parallel to a side of a
triangle intersects the other two sides, then it divides those sides
proportionally.
• Triangle Angle Bisector Theorem - An angle bisector of a triangle
divides the opposite side into two segments whose lengths are
proportional to the lengths of the other two sides.
• Two Transversal Proportionality Corollary - If three or more parallel lines intersect two transversals, then they divide
the transversals proportionally.
a
• Proportional Perimeters and Areas Theorem - If the similarity ratio of two similar figures is ! b , then the ratio of their
2
perimeters is ! ba and the ratio of their areas is ! ba2 or !
• Properties of Similarity
• Reflexive Property of Similarity
• Transitive Property of Similarity
! ΔABC
( ba )2
∼ ΔABC
If ! ΔABC ∼ ΔDEF and ! ΔDEF ∼ ΔXYZ , then ! ΔABC ∼ ΔXYZ .
Geometry
Chapter 7 Practice Problems
1) Two rectangles are similar. They both have a width to
length ratio of 2:3. The ratio of the lengths between the
rectangles is 3:1. The larger rectangle has a perimeter of
90 miles. Find the area of each rectangle.
Name: ______________________________________
Date: ____________________ Period: ____________
2) Explain why the triangles are similar and find the length
of DE.
!
Reason:
Area of smaller = ___________
Area of larger = ____________
DE = ___________
3) Find KN and LM.
4) Find the lengths BE and DE.
!
!
KN = _______
BE = ________
LM = _______
DE = ________
5) In ! ΔQRS , the bisector of ! ∠R divides ! QS into
segments with lengths 2.1 and 2.8. If RQ = 3, what is the
6) Given that ! DEFG
area of WXYZ.
∼ WXYZ , find the perimeter and
length of ! RS ? Draw a diagram and solve.
!
RS = _________
Perimeter = __________
7) A free-fall ride at an amusement park casts a shadow
Area = ___________
8) Given that ! ΔPQR ∼ ΔPST , find the scale factor and
the coordinates of S.
! 43
2
feet long. At the same time, a 6-foot-tall person
3
standing in line casts a shadow 2 feet long. What is the
height of the ride?
!
Scale factor = ______
Height of ride = __________
S = ___________