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Honors Geometry

In this assignment, we focus on special right triangles—45-45-90 and 30-60-90 triangles. You will learn to find the side lengths of these triangles and apply them to real-world problems. We begin with a warm-up exercise to solve equations and express answers in simplified radical form. Then, we explore the properties of these triangles, including how to find the hypotenuse and side lengths. We conclude with a checkpoint question to reinforce learning and a homework practice worksheet to solidify your understanding.

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Honors Geometry

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  1. Honors Geometry 9.4 Special Right Triangles

  2. 9.1 – 9.3 Assignment Check • RQS QTS RTQ • QS • TS=6 • SQ=2 3 • 4 2 • 12 • 4 35 • No; (60.5) + (60.5) 90

  3. Learning Goals Today you will: • Find the side lengths of special right triangles • Use special right triangles to solve real-world problems

  4. Warm Up Solve the equation for the missing variable. Assume all variables are positive. Express the answer in simplified radical form. 1. 2. 3.

  5. Quilt Squares

  6. 45-45-90 Triangle Theorem In a 45-45-90 triangle, the hypotenuse is times as long as each leg.

  7. 30-60-90 Triangle Theorem In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg.

  8. Finding the Hypotenuse in a 45-45-90 Triangle

  9. Side Lengths in a 30-60-90 Triangle

  10. On Your Own

  11. The Altitude of an Equilateral Triangle

  12. Area of a Square Find the area of a square with a diagonal length of

  13. Checkpoint Find the value of each variable. Write answer in simplest radical form.

  14. Closure Find the ratio of the lengths of the sides of a 30°-60°-90° triangle and of a 45°-45°-90° triangle.

  15. Homework 9.4 Practice C Worksheet

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