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Unit 7 · Right Triangles and Trigonometry

7.545-45-90 Triangles

Quick Answer

In a 45-45-90 triangle, the legs are equal and the hypotenuse = leg × √2. Given the hypotenuse, each leg = hypotenuse / √2 = hypotenuse × (√2/2).

Essential Question

Why does the hypotenuse of a 45-45-90 triangle always equal the leg times √2, and how do you move between leg and hypotenuse?

Learning Goals

  • 1State the 45-45-90 side ratios.
  • 2Find the hypotenuse given a leg.
  • 3Find a leg given the hypotenuse.
  • 4Recognize 45-45-90 triangles in context.

Key Vocabulary

45-45-90 triangle

An isosceles right triangle with side ratios 1 : 1 : √2.

Isosceles right triangle

A right triangle with two congruent legs and a 45° angle at each base.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.