Geometry 8-2a GeoGebra Primer: Special Right Triangles

PART 1: Interact with the GeoGebra applet below before responding to the items that follow.

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Exploration: How would you classify the triangle above by its sides?

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Exploration: What is the measure of the gray angle in degrees? Enter only a number.

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Exploration: What is the measure of each acute pink angle in degrees? Enter only a number.

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Exploration: What are the measures of the triangle's interior angles? List them from least to greatest in this format: 21, 25, 93

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Exploration: Suppose the thick black segment in the triangle measures 3 inches. Algebraically determine the length of the longest side in simplest radical form.

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Exploration: Suppose the thick black segment in the triangle measures 4 inches. Algebraically determine the length of the longest side in simplest radical form. Enter your response in this format: 5sqrt(3)

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Exploration: Suppose the thick black segment in the triangle measures 5 inches. Algebraically determine the length of the longest side in simplest radical form. Enter your response in this format: 5sqrt(3)

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Extension: You should notice a pattern in the relationship between side lengths. Describe the pattern as it relates to this specific type of right triangle, a 45-45-90 triangle.

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Extension: Suppose the thick black segment has length a. What is the length of the longest side in simplest radical form? Use the same formatting as before.

PART 2: Interact with the GeoGebra applet below before responding to the items that follow.

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Exploration: Suppose the measure of ∠A is x. What is measure of ∠B, in terms of x?

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Exploration: Suppose the measure of ∠A is x. What is the measure of ∠C, in terms of x?

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Exploration: Use algebra to find m∠A. Enter only a number (of degrees).

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Exploration: Use algebra to find m∠B. Enter only a number (of degrees).

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Exploration: Use algebra to find m∠C. Enter only a number (of degrees).

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Exploration: How does the length of the hypotenuse of this 30-60-90 triangle compare with the length of this triangle's shorter leg?

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Exploration: Suppose the shorter leg's length (BC) = 4. What is AB? Enter only a number.

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Exploration: Suppose BC = 5. What is AB? Enter only a number.

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Extension: Use the developing pattern to make a conjecture about the relationship between lengths of the shorter and longer legs of a 30-60-90 triangle.

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Exploration: Given BC = 5 and AB = 10 calculate AC in simplest radical form.

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Exploration: Given BC = 6 and AB = 12 calculate AC in simplest radical form.

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Exploration: Given BC = 7 and AB = 14 calculate AC in simplest radical form.

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Extension: Use the developing pattern to make a conjecture about the relationship between length of the shorter leg of a 30-60-90 triangle and the length of the hypotenuse.

20

Geometry 8-2a GeoGebra Primer: Special Right Triangles

Exploration: How would you classify the triangle above by its sides?

Exploration: What is the measure of the gray angle in degrees? Enter only a number.

Exploration: What is the measure of each acute pink angle in degrees? Enter only a number.

Exploration: What are the measures of the triangle's interior angles? List them from least to greatest in this format: 21, 25, 93

Exploration: Suppose the thick black segment in the triangle measures 3 inches. Algebraically determine the length of the longest side in simplest radical form.

Exploration: Suppose the thick black segment in the triangle measures 4 inches. Algebraically determine the length of the longest side in simplest radical form. Enter your response in this format: 5sqrt(3)

Exploration: Suppose the thick black segment in the triangle measures 5 inches. Algebraically determine the length of the longest side in simplest radical form. Enter your response in this format: 5sqrt(3)

Extension: You should notice a pattern in the relationship between side lengths. Describe the pattern as it relates to this specific type of right triangle, a 45-45-90 triangle.

Extension: Suppose the thick black segment has length a. What is the length of the longest side in simplest radical form? Use the same formatting as before.

Exploration: Suppose the measure of ∠A is x. What is measure of ∠B, in terms of x?

Exploration: Suppose the measure of ∠A is x. What is the measure of ∠C, in terms of x?

Exploration: Use algebra to find m∠A. Enter only a number (of degrees).

Exploration: Use algebra to find m∠B. Enter only a number (of degrees).

Exploration: Use algebra to find m∠C. Enter only a number (of degrees).

Exploration: How does the length of the hypotenuse of this 30-60-90 triangle compare with the length of this triangle's shorter leg?

Exploration: Suppose the shorter leg's length (BC) = 4. What is AB? Enter only a number.

Exploration: Suppose BC = 5. What is AB? Enter only a number.

Extension: Use the developing pattern to make a conjecture about the relationship between lengths of the shorter and longer legs of a 30-60-90 triangle.

Exploration: Given BC = 5 and AB = 10 calculate AC in simplest radical form.

Exploration: Given BC = 6 and AB = 12 calculate AC in simplest radical form.

Exploration: Given BC = 7 and AB = 14 calculate AC in simplest radical form.

Extension: Use the developing pattern to make a conjecture about the relationship between length of the shorter leg of a 30-60-90 triangle and the length of the hypotenuse.

Extension: Suppose the shortest leg of a 30-60-90 triangle has length a. What is the length of the hypotenuse in simplest radical form?

Exploration: How would you classify the triangle above by its sides?

Exploration: What is the measure of the gray angle in degrees? Enter only a number.

Exploration: What is the measure of each acute pink angle in degrees? Enter only a number.

Exploration: What are the measures of the triangle's interior angles? List them from least to greatest in this format: 21, 25, 93

Exploration: Suppose the thick black segment in the triangle measures 3 inches. Algebraically determine the length of the longest side in simplest radical form.

Exploration: Suppose the thick black segment in the triangle measures 4 inches. Algebraically determine the length of the longest side in simplest radical form. Enter your response in this format: 5sqrt(3)

Exploration: Suppose the thick black segment in the triangle measures 5 inches. Algebraically determine the length of the longest side in simplest radical form. Enter your response in this format: 5sqrt(3)

Extension: You should notice a pattern in the relationship between side lengths. Describe the pattern as it relates to this specific type of right triangle, a 45-45-90 triangle.

Extension: Suppose the thick black segment has length a. What is the length of the longest side in simplest radical form? Use the same formatting as before.

Exploration: Suppose the measure of ∠A is x. What is measure of ∠B, in terms of x?

Exploration: Suppose the measure of ∠A is x. What is the measure of ∠C, in terms of x?

Exploration: Use algebra to find m∠A. Enter only a number (of degrees).

Exploration: Use algebra to find m∠B. Enter only a number (of degrees).

Exploration: Use algebra to find m∠C. Enter only a number (of degrees).

Exploration: How does the length of the hypotenuse of this 30-60-90 triangle compare with the length of this triangle's shorter leg?

Exploration: Suppose the shorter leg's length (BC) = 4. What is AB? Enter only a number.

Exploration: Suppose BC = 5. What is AB? Enter only a number.

Extension: Use the developing pattern to make a conjecture about the relationship between lengths of the shorter and longer legs of a 30-60-90 triangle.

Exploration: Given BC = 5 and AB = 10 calculate AC in simplest radical form.

Exploration: Given BC = 6 and AB = 12 calculate AC in simplest radical form.

Exploration: Given BC = 7 and AB = 14 calculate AC in simplest radical form.

Extension: Use the developing pattern to make a conjecture about the relationship between length of the shorter leg of a 30-60-90 triangle and the length of the hypotenuse.

Extension: Suppose the shortest leg of a 30-60-90 triangle has length a. What is the length of the hypotenuse in simplest radical form?