30-60-90 triangle discovery

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Who is in your group (first and last names)?

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Sketch an equilateral triangle. Draw a perpendicular bisector from your top vertex to the bottom side, making two right triangles. Fill in the all of the angle measures using your knowledge of equilateral triangles and bisectors. If one side is 10 inches, fill in as many sides and pieces of sides as possible.

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What similarity theorem(s) explain how all 30-60-90 triangles are similar? Select all correct answer(s):

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Consider one side of the equilateral triangle you just made in the orientation below. How can you represent x in terms of a?

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Use the Pythagorean Theorem on the triangle below to express y in terms of a. Be sure to reduce and rationalize radicals.

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Without using the Pythagorean Theorem, find the missing side lengths of a 30-60-90 triangle if the hypotenuse is 8 units long. Draw the triangle, fill in the angles, then fill in the missing sides.

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In a 45-45-90 triangle, the hypotenuse is ____ times as long as a leg.

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A 45-45-90 triangle is a(n) _ triangle, so the legs are _.

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In a 30-60-90 triangle, the hypotenuse is ____ times as long as the shortest leg.

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In a 30-60-90 triangle, the longer leg is ____ times as long as the shortest leg.

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In a 30-60-90 triangle, the shortest side is across from the smallest angle.

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Find the value of x using your special right triangle formulas, you must show your work below to get full credit:

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What is the value of x?

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Find the value of x using your special right triangle formulas, you must show your work below to get full credit:

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What is the value of x?

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Find the value of x using your special right triangle formulas, you must show your work below to get full credit:

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What is the exact value of x?

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Find the values of x and y, clearly note your work and solutions:

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Who is in your group (first and last names)?

What similarity theorem(s) explain how all 30-60-90 triangles are similar? Select all correct answer(s):

Consider one side of the equilateral triangle you just made in the orientation below. How can you represent x in terms of a?

Use the Pythagorean Theorem on the triangle below to express y in terms of a. Be sure to reduce and rationalize radicals.

Without using the Pythagorean Theorem, find the missing side lengths of a 30-60-90 triangle if the hypotenuse is 8 units long. Draw the triangle, fill in the angles, then fill in the missing sides.

In a 45-45-90 triangle, the hypotenuse is ____ times as long as a leg.

A 45-45-90 triangle is a(n) _____ triangle, so the legs are _____.

In a 30-60-90 triangle, the hypotenuse is ____ times as long as the shortest leg.

In a 30-60-90 triangle, the longer leg is ____ times as long as the shortest leg.

In a 30-60-90 triangle, the shortest side is across from the smallest angle.

Find the value of x using your special right triangle formulas, you must show your work below to get full credit:

What is the value of x?

Find the value of x using your special right triangle formulas, you must show your work below to get full credit:

What is the value of x?

Find the value of x using your special right triangle formulas, you must show your work below to get full credit:

What is the exact value of x?

Find the values of x and y, clearly note your work and solutions:

Find the values of x and y, clearly note your work and solutions:

A 45-45-90 triangle is a(n) _ triangle, so the legs are _.