Geometric figures are similar if their corresponding (matching) angles are congruent (equal in
measure) and the ratio of their corresponding sides are in proportion.
What does proportional mean?
Facts about similar triangles
Angle A is congruent to angle D
Angle B is congruent to angle E
Angle C is congruent to angle F
The ratio of the corresponding sides is called the scale factor. The mathematical symbol used to
denote similarity is .
Example 1: The sides of a triangle are 5, 6 and 10. Find the length of the longest side of a
similar triangle whose shortest side is 15.
Example 2: The sides of a triangle are 7, 14 and 30. Find the length of the shortest side of a
similar triangle whose longest side is 90.
Example 3: In the diagram, Μ…Μ…Μ…Μ…
DE is parallel to Μ…Μ…Μ…Μ…
AC, BD = 4, DA = 6 and EC = 8. Find BC to the
nearest tenth.
Example 4: Two triangles are similar. The sides of the first triangle are 7, 9, and 11. The
smallest side of the second triangle is 21. Find the perimeter of the second triangle.
Example 5: Find BC
Example 6: Two ladders are leaned against a wall such that they make the same angle with the
ground. The 10' ladder reaches 8' up the wall. How much further up the wall does the 18'
ladder reach?
Example 7: In the diagram below of ΔADE, B is a point on
, and C is a point on
, AC = x − 3, BE = 20, AB = 16, and AD = 2x + 2. Find the length of
Example 8: Find the value of x in the following diagram
such that