Geometry 8-2a GeoGebra Primer: Special Right Triangles
By Matt Richardson
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Last updated about 3 years ago
23 Questions
PART 1: Interact with the GeoGebra applet below before responding to the items that follow.
10 points
10
Question 1
1.
Exploration: How would you classify the triangle above by its sides?
Exploration: How would you classify the triangle above by its sides?
10 points
10
Question 2
2.
Exploration: What is the measure of the gray angle in degrees? Enter only a number.
Exploration: What is the measure of the gray angle in degrees? Enter only a number.
10 points
10
Question 3
3.
Exploration: What is the measure of each acute pink angle in degrees? Enter only a number.
Exploration: What is the measure of each acute pink angle in degrees? Enter only a number.
10 points
10
Question 4
4.
Exploration: What are the measures of the triangle's interior angles? List them from least to greatest in this format: 21, 25, 93
Exploration: What are the measures of the triangle's interior angles? List them from least to greatest in this format: 21, 25, 93
10 points
10
Question 5
5.
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 3 inches. Algebraically determine the length of the longest side in simplest radical form.
10 points
10
Question 6
6.
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 4 inches. Algebraically determine the length of the longest side in simplest radical form. Enter your response in this format: 5sqrt(3)
10 points
10
Question 7
7.
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)
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)
20 points
20
Question 8
8.
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: 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.
20 points
20
Question 9
9.
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.
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.
10 points
10
Question 10
10.
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 measure of ∠B, in terms of x?
10 points
10
Question 11
11.
Exploration: Suppose the measure of ∠A is x. What is the measure of ∠C, in terms of x?
Exploration: Suppose the measure of ∠A is x. What is the measure of ∠C, in terms of x?
10 points
10
Question 12
12.
Exploration: Use algebra to find m∠A. Enter only a number (of degrees).
Exploration: Use algebra to find m∠A. Enter only a number (of degrees).
10 points
10
Question 13
13.
Exploration: Use algebra to find m∠B. Enter only a number (of degrees).
Exploration: Use algebra to find m∠B. Enter only a number (of degrees).
10 points
10
Question 14
14.
Exploration: Use algebra to find m∠C. Enter only a number (of degrees).
Exploration: Use algebra to find m∠C. Enter only a number (of degrees).
10 points
10
Question 15
15.
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: How does the length of the hypotenuse of this 30-60-90 triangle compare with the length of this triangle's shorter leg?
10 points
10
Question 16
16.
Exploration: Suppose the shorter leg's length (BC) = 4. What is AB? Enter only a number.
Exploration: Suppose the shorter leg's length (BC) = 4. What is AB? Enter only a number.
10 points
10
Question 17
17.
Exploration: Suppose BC = 5. What is AB? Enter only a number.
Exploration: Suppose BC = 5. What is AB? Enter only a number.
20 points
20
Question 18
18.
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.
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.
10 points
10
Question 19
19.
Exploration: Given BC = 5 and AB = 10 calculate AC in simplest radical form.
Exploration: Given BC = 5 and AB = 10 calculate AC in simplest radical form.
10 points
10
Question 20
20.
Exploration: Given BC = 6 and AB = 12 calculate AC in simplest radical form.
Exploration: Given BC = 6 and AB = 12 calculate AC in simplest radical form.
10 points
10
Question 21
21.
Exploration: Given BC = 7 and AB = 14 calculate AC in simplest radical form.
Exploration: Given BC = 7 and AB = 14 calculate AC in simplest radical form.
20 points
20
Question 22
22.
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: 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 points
20
Question 23
23.
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?
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?