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MM2G1. Students will identify and use special right triangles.

Learn to identify and apply special right triangles: 30-60-90 and 45-45-90. Use Pythagorean theorem to find missing sides expressed as radicals. Understand proportions within these triangles.

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MM2G1. Students will identify and use special right triangles.

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  1. Standards MM2G1. Students will identify and use special right triangles. a. Determine the lengths of sides of 30°-60°-90° triangles. b. Determine the lengths of sides of 45°-45°-90° triangles.

  2. MM2G1a. Determine the lengths of sides of 30°-60°-90° triangles. b. Determine the lengths of sides of 45°-45°-90° triangles. Use the Pythagorean theorem to find the missing side of each right triangle. Express your answers as a radicals in simplest form.

  3. MM2G1a. Determine the lengths of sides of 30°-60°-90° triangles. b. Determine the lengths of sides of 45°-45°-90° triangles. • What do you notice about the legs of each triangle? • These triangles are called ________________ triangles. They are also known as 45-45-90 triangles because: • What do you notice about the hypotenuse with respect to each leg??

  4. MM2G1a. Determine the lengths of sides of 30°-60°-90° triangles. b. Determine the lengths of sides of 45°-45°-90° triangles. Use the Pythagorean theorem to find the missing side of each right triangle. Express your answers as a radicals in simplest form.

  5. MM2G1a. Determine the lengths of sides of 30°-60°-90° triangles. b. Determine the lengths of sides of 45°-45°-90° triangles. • What do you notice about the legs of each triangle? • These triangles are called 30-60-90 triangles because: • What do you notice about the hypotenuse with respect to each leg??

  6. MM2G1a. Determine the lengths of sides of 30°-60°-90° triangles. b. Determine the lengths of sides of 45°-45°-90° triangles. • In a 45-45-90 right triangle, the hypotenuse is _______ times as long as each leg.

  7. MM2G1a. Determine the lengths of sides of 30°-60°-90° triangles. b. Determine the lengths of sides of 45°-45°-90° triangles. • In a 30-60-90 right triangle, the hypotenuse is _______ as long as the shorter leg, and the longer leg is ______ times as long as the shorter leg. • ALWAYS FIND THE SHORTEST LEG FIRST!!

  8. Determine if the triangle is a 45-45-90 triangle, or a 30-60-90 triangle. Then find the value of the variable. 1) type of triangle: x =

  9. Determine if the triangle is a 45-45-90 triangle, or a 30-60-90 triangle. Then find the value of the variable. 2) type of triangle: x =

  10. Determine if the triangle is a 45-45-90 triangle, or a 30-60-90 triangle. Then find the value of the variable. 3) type of triangle: x =

  11. Determine if the triangle is a 45-45-90 triangle, or a 30-60-90 triangle. Then find the value of the variable. 4) type of triangle: x =

  12. Determine if the triangle is a 45-45-90 triangle, or a 30-60-90 triangle. Then find the value of the variable. 5) type of triangle: x =

  13. Determine if the triangle is a 45-45-90 triangle, or a 30-60-90 triangle. Then find the value of the variable. 6) type of triangle: x = y =

  14. HOMEWORK!! Pg. 153 – 154: 1 – 22 ALL DRAW FIGURES AND SHOW WORK FOR CREDIT!!

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