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**Standard(s): **
[MA2019] GEO-19 (9-12) 35 :

35. Discover and apply relationships in similar right triangles.

a. Derive and apply the constant ratios of the sides in special right triangles (45^{o}-45^{o}-90^{o} and 30^{o}-60^{o}-90^{o}).

b. Use similarity to explore and define basic trigonometric ratios, including sine ratio, cosine ratio, and tangent ratio.

c. Explain and use the relationship between the sine and cosine of complementary angles.

d. Demonstrate the converse of the Pythagorean Theorem.

e. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems, including finding areas of regular polygons.

This video will be used to re-enforce the relationships between the sides and angles in special right triangles. The video has a catchy song that will help students remember the relationships.

*This activity results from the ALEX Resource Development Summit.*

35. Discover and apply relationships in similar right triangles.

a. Derive and apply the constant ratios of the sides in special right triangles (45^{o}-45^{o}-90^{o} and 30^{o}-60^{o}-90^{o}).

b. Use similarity to explore and define basic trigonometric ratios, including sine ratio, cosine ratio, and tangent ratio.

c. Explain and use the relationship between the sine and cosine of complementary angles.

d. Demonstrate the converse of the Pythagorean Theorem.

e. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems, including finding areas of regular polygons.

In this Desmos activity, students are guided through a series of questions to verify the relationships between the sides and angles of a 30°-60°-90° right triangle and a 45°-45°-90° triangle. This is intended to be a during activity for a lesson on discovering and applying relationships in similar right triangles.

*This activity results from the ALEX Resource Development Summit.*

35. Discover and apply relationships in similar right triangles.

a. Derive and apply the constant ratios of the sides in special right triangles (45^{o}-45^{o}-90^{o} and 30^{o}-60^{o}-90^{o}).

b. Use similarity to explore and define basic trigonometric ratios, including sine ratio, cosine ratio, and tangent ratio.

c. Explain and use the relationship between the sine and cosine of complementary angles.

d. Demonstrate the converse of the Pythagorean Theorem.

e. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems, including finding areas of regular polygons.

In this Desmos activity, students will explore the special relationships between the sides of a 30-60-90 triangle and a 45-45-90 triangle. This is intended to be a before activity for a lesson on the relationships of special right triangles and their connection to trigonometry.

*This activity results from the ALEX Resource Development Summit.*