Similar Polygons

1
Similar Polygons

• Lesson 7.3
• Pre-AP Geometry

2
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.

3
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.

4
Similar Polygons

• Given Quadrilateral ABCD quadrilateral EFGH.
  
• 1. Name the pairs of corresponding equal
  angles.
• 2. Give the ratios of all corresponding sides.

5
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).

6
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 (33?53).

7
Similar Polygons

• Quadrilateral ABCD quadrilateral EFGH.
• (a) Find m ? E.
• (b) Find x.

8
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.
• Here ABC ? A'B'C'

9
Scale Factor

• In similar polygons, the ratio of the lengths of
  any two corresponding sides is called the scale
  factor.
• Scale Factor Video

10
Similar Polygons

• Problem 1 Quad. ABCD ? Quad ABCD where
  AB y, BC 22, CD 50, AD 30, AB
  12, BC z, CD 30, AD x.
• Find (a) the scale factor (b) the values of x,
  y, and z (c) the ratio of the perimeters.

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Similar Polygons

• Problem 2 Quad. EFGH ? Quad. EFGH where EH
  12, HG 5, GF y, EF 10, EH x, HG
  2.5, GF 3, EF z.
• Find (a) the scale factor (b) the values of x,
  y, and z (c) the ratio of the perimeters.

12
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 ____

13
Written Exercises

• Problem Set 7.3A, p.250 2 - 22 (even)

14
Written Exercises

• Problem Set 7.3B, Handout 7-3