Introduction to Similar Triangles

• Similar figures


  Figures with the same shape
• Congruent figures


  Figures with the same shape and same size
• Congruent figures are also similar figures
• Similar figures


  • Corresponding angles are congruent
  • Corresponding sides are proportional
• Congruent figures


  • Corresponding angles are congruent
  • Corresponding sides are congruent
• Similar to symbol


  Denotes similar figures
• Congruent to symbol


  Denotes congruent figures
• Similar triangles


  • Have the same shape
  • Corresponding angles are congruent
  • Corresponding sides are proportional
• Determining if triangles are similar


  1. Corresponding angles are congruent

  2. Corresponding sides are proportional
• Similarity ratio


  The simplest form of the ratio of the length of two corresponding sides of similar triangles
• Scale factor


  The amount of enlargement or reduction needed to get a similar figure from the other<|>The ratio of the dimension of an object in its diagonal image to its actual size
• When scale factor is less than 1

  The similar figure is a reduction
• When scale factor is greater than 1


  The similar figure is an enlargement
• Finding the shortest side of a reduced triangle

  1. Use the fundamental law of proportion

  2. Shortest side of reduced triangle = (Shortest side of original triangle) / Scale factor
• The measure of a corresponding angle in similar triangles is the same
• The similarity ratio of similar triangles is the ratio of the lengths of any pair of corresponding sides
• Finding the measure of a side in similar triangles

  1. Use the fundamental law of proportion

  2. Side length = (Corresponding side length) x (Similarity ratio)