Special Relationships Within Right Triangles—Dividing into Two Similar Sub-Triangles

Why are right triangles so special? Pupils begin their study of right triangles by examining similar right triangles. Verifying through proofs, scholars recognize the three similar right triangles formed by drawing the altitude. Once verified, pupils use the relationship to find missing side lengths. 

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CCSS: Designed
Additional Tags
Instructional Ideas
  • Allow learners to struggle with finding the side lengths created by drawing the altitude; using the side lengths of the original triangle, they should eventually be able to develop a strategy to find the other sides
  • Incorporate board work to allow frequent checks for understanding when using notation and writing and solving proportions
Classroom Considerations
  • Pupils should be comfortable writing and solving proportions based on triangle proportionality
  • Continues the series of 36 lessons on similarity
  • Inquiry-based lesson that allows scholars to test their own strategies
  • Includes scaffolding suggestions for struggling learners
  • None
Common Core