Similar Polygons

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Similar Polygons
Lesson 7.3
Pre-AP Geometry
Lesson Focus
This lesson introduces one of the major topics in geometry,
the study of similar figures. Congruent figures have the same
size and shape. Similar figures have the same shape.
Similar Polygons
Two polygons with the same shape are called similar
polygons.
The symbol for “is similar to” is ∼. (Example: ABC  EFG)
(Notice that  is a portion of the “is congruent to” symbol, ≅.)
When two polygons are similar, these two facts both must be
true:
– Corresponding angles are equal.
– The ratios of pairs of corresponding sides must all be
equal.
Similar Polygons
Given: Quadrilateral ABCD ∼ quadrilateral EFGH.
1. Name the pairs of corresponding equal angles.
2. Give the ratios of all corresponding sides.
Similar Polygons
It is possible for a polygon to have one of the above facts true
without having the other fact true.
Quadrilateral QRST is not similar to quadrilateral WXYZ.
Even though the ratios of corresponding sides are equal,
corresponding angles are not equal (90° ≠ 120°, 90° ≠ 60°).
Similar Polygons
Quadrilateral FGHI is not similar to quadrilateral JKLM.
Even though corresponding angles are equal, the ratios of
each pair of corresponding sides are not equal (3:3≠5:3).
Similar Polygons
Quadrilateral ABCD ∼ quadrilateral EFGH.
(a) Find m ∠ E.
(b) Find x.
Similar Polygons
It is common to label each corner with letters, and to use a
little dash (called a Prime) to mark each corner of the
reflected image.
A
A’
B’
B
C
Here ABC  A'B'C'
C’
Scale Factor
In similar polygons, the ratio of the lengths of any two
corresponding sides is called the scale factor.
Scale Factor Video
Similar Polygons
Problem #1: Quad. ABCD  Quad A’B’C’D’ where AB = y,
BC = 22, CD = 50, AD = 30, A’B’ = 12, B’C’ = z, C’D’ = 30, A’D’ =
x.
Find: (a) the scale factor; (b) the values of x, y, and z; (c) the
ratio of the perimeters.
Similar Polygons
Problem #2: Quad. EFGH  Quad. E’F’G’H’ where EH = 12,
HG = 5, GF = y, EF = 10, E’H’ = x, H’G’ = 2.5, G’F’ = 3, E’F’ = z.
Find: (a) the scale factor; (b) the values of x, y, and z; (c) the
ratio of the perimeters.
Similar Polygons
Problem #3: Quad. ABCD  Quad. EFGH where AD = 5, DC = 4,
mA = 60, mC = 90, EF = 21, FG = 6, HG = 12, mF = 100.
Find: (a) mE = ____
(b) mG = ____
(c) mB = ____
(d) If mD = 110, then mH = ____.
(e) The scale factor is ____.
(f) EH = ____
(g) BC = ____
(h) AB = ____
Written Exercises
Problem Set 7.3A, p.250: # 2 - 22 (even)
Written Exercises
Problem Set 7.3B, Handout 7-3
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