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Shortcut Methods for Similar Triangles

Discover shortcut methods for determining similar triangles and use proportions to find measures in similar figures. Practice problems included.

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Shortcut Methods for Similar Triangles

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  1. Do Now • Take out your 11.1 Worksheet ready to be stamped. • Take out a compass and protractor. • What does it mean for polygons to be similar? • Give a counterexample to each statement. (Can be in the form of a picture or explanation.) • Two polygons that have corresponding angles congruent must be similar. • Two polygons that have corresponding sides proportional must be similar.

  2. Announcements • 11.2 WS is due Wednesday • Parts 1-2 of the house project are due Wednesday • Bring your raffle tickets for an auction on Wednesday • Bring your compasses every day next week

  3. Similar Triangles

  4. Today’s Objectives • Discover shortcut methods for determining similar triangles • Use proportions to find measures in similar figures • Use problem solving skills

  5. Based on last class… • We concluded that you must know about both the angles and the sides of two polygons in order to make a valid conclusion about their similarity. • However, triangles are unique. Remember there were 4 shortcuts for triangle congruence: SSS, SAS, ASA, and SAA. • Are there shortcuts for similarity also?

  6. Suppose two triangles had one corresponding angle congruent. Would the triangles be similar?

  7. Is AA a Similarity Shortcut?

  8. From the second step in the investigation you see there is no need to check AAA, ASA, or SAA similarity conjectures. • Because of the Triangle Sum Conjecture and the Third Angle Conjecture AA Similarity Conjecture is all you need.

  9. Is SSS a Similarity Shortcut?

  10. So SSS, AAA, ASA and SAA are shortcuts for triangle similarity.

  11. Is SAS a Similarity Shortcut?

  12. Practice

  13. Practice

  14. Practice

  15. Today’s Objectives • Discover shortcut methods for determining similar triangles • Use proportions to find measures in similar figures • Use problem solving skills

  16. Exit Slip 1. Find the missing values. Show your work and Explain your reasoning 2. Write the similarity statement and give a proof of why the triangles are similar.

  17. Honors Exit Slip 1. Find the missing values. Show your work and Explain your reasoning 2. Write the similarity statement and give a proof of why the triangles are similar.

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