CONGRUENT AND SIMILAR FIGURES

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UNIT 23

• CONGRUENT AND SIMILAR FIGURES

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CONGRUENT FIGURES

• Congruent figures have exactly the same size and
  shape. The symbol ? means congruent
• Corresponding parts of congruent triangles are
  equal
• The sides that lie opposite equal angles are
  corresponding sides
• The angles that lie opposite equal sides are
  corresponding angles

• ?BCA and ?CAD in the figure shown on the
• left are corresponding angles because they
  are
• both opposite 5" long sides

• ?BAC and ?ACD are also corresponding angles
  because they are both opposite 4.75" long sides

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SIMILAR FIGURES

• Similar figures mean figures that are alike in
  shape but different in size
• Similar polygons have the same number of sides,
  equal corresponding angles, and proportional
  corresponding sides
• The symbol means similar
• Corresponding angles of similar polygons are
  equal
• Corresponding sides of similar polygons are
  proportional

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SIMILAR FIGURE EXAMPLE

• Given that the two polygons shown below are
  similar and ?A ?A', ?B ?B', ?C ?C', and ?D
  ?D, determine the lengths of sides (a) A'B',
  (b) B'C', and (c) C'D'

• The corresponding sides are proportional

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SIMILAR TRIANGLES

• If two angles of a triangle are equal to two
  angles of another triangle, the triangles are
  similar
• If the corresponding sides of two triangles are
  proportional, the triangles are similar
• If two sides of a triangle are proportional to
  two sides of another triangle and if the angles
  included between these sides are equal, the
  triangles are similar
• Within a triangle, if a line is parallel to one
  side and intersects the other two sides, the
  triangle formed and the given triangle are similar

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SIMILAR TRIANGLES EXAMPLE

• If the altitude is drawn to the hypotenuse of a
  right triangle, the two triangles formed are
  similar to each other and to the given triangle
• Determine AD and DC in the right triangle shown
  below

• BD ? AC so ?ABC ?ABD ?BDC

DC AC AD 25 mm 16 mm 9 mm Ans
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PRACTICE PROBLEMS

• 1. Identify the pairs of corresponding angles in
  the figure below

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PRACTICE PROBLEMS

• 2. The two polygons below are similar. ?A ?A?,
  ?B ?B?, ?C ?C?, ?D ?D?, ?E ?E?, ?F ?F?.
  Find each of the following
• a) Side BC
• b) Side CD
• c) Side DE
• d) Side AF

A?
10"
11"
B?
13.5"
F?
9"
C?
E?
12.5"
11.5"
D?
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PRACTICE PROBLEMS

• 3. ?CDE ?ABE in the figure below. Given that
  AE 70 ft, BE 87.5 ft, EC 25 ft, ED 20 ft,
  and CD 40 ft, find AB.

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PRACTICE PROBLEMS

• 4. Determine length F in the figure below given
  that AB 32 m and AC 10 m.

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PROBLEM ANSWER KEY

• 1. ?ABE and ?CED
• ?AEB and ?ECD
• ?BAE and ?EDC
• 2. a) 10.8 inches
• b) 10 inches
• c) 9.2 inches
• d) 8.8 inches
• 3. 140 feet
• 4. 15.625 m