Special Right Triangles

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Special Right Triangles

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Presentation transcript:

Special Right Triangles 30 – 60 – 90 45 – 45 – 90

Geogebra Activity Answers

30 – 60 – 90 Triangle From the Geogebra Activity we know that the “30 – 60 – 90 Triangle” comes from splitting an equilateral triangle in half. Now lets look at a comparison of the sides using the Pythagorean Theorem.

30 – 60 – 90 Triangle Because this special rt. triangle comes from an equilateral triangle, the hypotenuse must be 2 times as long as the short leg. Can we use the Pythagorean Theorem to find the long leg? 𝑎 2 + 𝑏 2 = 𝑐 2 2cm 1cm

30 – 60 – 90 Triangle Therefore, the side-length ratios of : short leg: long leg: hypotenuse are 1 : 3 :2 or 𝑥 :𝑥 3 :2𝑥 These will always hold true for 30 – 60 – 90 Triangles!! Memorize them!!

45 – 45 – 90 Triangle From the Geogebra Activity we know that the “45 – 45 – 90 Triangle” comes from splitting a square in half from corner to corner. Now lets look at a comparison of the sides using the Pythagorean Theorem.

45 – 45 – 90 Triangle Because this special rt. triangle comes from a square, both legs must be the same exact length. Can we use the Pythagorean Theorem to find the hypotenuse? 𝑎 2 + 𝑏 2 = 𝑐 2 1cm 1cm

45 – 45 – 90 Triangle Therefore, the side-length ratios of : leg: leg: hypotenuse are 1 :1 : 2 or 𝑥 :𝑥 :𝑥 2 These will always hold true for 45 – 45 – 90 Triangles!! Memorize them!!

But how do I keep them separate? 30 – 60 – 90 Triangle: 𝟏 : 𝟑 :𝟐 (it’s the one with the 3 in both… “30” and “ 3 ”) 45 – 45 – 90 Triangle: 𝟏 :𝟏 : 𝟐 (the “45’s” repeat and so do the “1’s”)

Practice Find the missing sides: Example 1: 5 ft 30 Type of Sp. Rt. Tri. : Find the missing sides: Example 1: 30 5 ft

Practice Find the missing sides: Example 2: 8 ft 60 Type of Sp. Rt. Tri. : Find the missing sides: Example 2: 60 8 ft

Practice Find the missing sides: Example 3: 13 cm 45 Type of Sp. Rt. Tri. : Find the missing sides: Example 3: 45 13 cm

Practice Find the missing sides: Example 3: 20 cm 45 Type of Sp. Rt. Tri. : Find the missing sides: Example 3: 45 20 cm