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Solving Problems with Similar Triangles in Geometry

Learn to determine and solve problems using the properties of similar triangles. Draw, label, and compare triangles to understand corresponding sides and angles. Use equal proportions to verify similarity and find missing side lengths.

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Solving Problems with Similar Triangles in Geometry

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  1. 3.0 Similar Triangles

  2. Focus on… • determine similar triangles • solve problems using the properties of similar triangles

  3. Similar Triangles • On a piece of graph paper draw two lines that join with a 90 degree angle. • Make one line 3cm and the other 4cm. 3 cm 4 cm

  4. Draw a third line to close the figure and make a triangle. • How long is the third line? 5 cm 3 cm 4 cm

  5. More… • Label your triangle’s vertex with A, B and C, so the shortest side is AB, the other short side is BC and the longest side is AC. A C B

  6. Draw a second right triangle, but this time the short sides are 6cm and 8cm. • How long is the longest side? 10 cm 6 cm 8 cm

  7. Label your second triangle with DEF. • Which sides on your small triangle correspond with the sides of your large triangle? D E F

  8. corresponding angles and corresponding sides have the same relative position in geometric figures

  9. Triangles ABC and DEF are Similar • What conditions do you think are necessary in order for two triangles to be similar?

  10. Similar Triangles • have the same shape but different size • have equal corresponding angles and proportional corresponding sides

  11. Are these similar?

  12. Use Equal Proportions… • AB = 12 • EF = 4 • To make 12 into 4, you divide by 3 • BC = 15 • FG = 5 • This also is dividing by 3 • So, since the proportions are equal on all sides, then the triangles are similar.

  13. Use Similar Triangles to Determine a Missing Side Length y

  14. Find the missing side

  15. Determine the missing side length.

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