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The leg of a right triangle is 4 units and the hypotenuse is 9 units. What is the length, in units, of the other leg of the triangle? (4 points)
square root 97 units
97 units
square root 65 units
65 units
2.
The legs of a right triangle are 5 units and 15 units. What is the length of the hypotenuse? (4 points)
200 units
square root 200 units
square root 250 units
250 units
3.
Ella calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle is it? (4 points)
Four triangles are shown. Triangle A has sides marked 3 and 5. Triangle B has sides marked 4 and 5. Triangle C has sides marked 2 and 4 and a right angle marked in between them. Triangle D has three equal sides, and two sides are marked 4 and 4.
A
B
C
D
4.
Look at points C and D on the graph:
A coordinate plane graph is shown. Point C is at 1 comma 3. Point D is at 4 comma negative 3. A segment connects the two points.
What is the distance (in units) between points C and D? Round your answer to the nearest hundredth. (4 points)
3.01 units
5.20 units
6.50 units
6.71 units
5.
The graph shows the location of Amber's, Betsey's, and Claire's houses. Each unit on the graph represents 1 block.
A coordinate plane graph is shown. Ambers house is located at negative 3 comma negative 3. Betseys house is located at 5 comma negative 3. Claires house is located at 5 comma 4.
If Amber walks from her house to Claire's house, then on to Betsey's house along the path shown, how far will she have walked in blocks? Round your answer to the nearest hundredth. (4 points)
15.32 blocks
17.63 blocks
18.63 blocks
113.00 blocks
6.
The sets of numbers 7, 24, 25 and 9, 40, 41 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples! (5 points)
7.
Cade and Tyce both tried to find the missing side of the right triangle.
A right triangle is shown. The legs are labeled 6 and 9. A right angle is labeled in between them.
Cade's Work Tyce's Work
a2 + b2 = c2 a2 + b2 = c2
62 + b2 = 92 62 + 92 = c2
36 + b2 = 81 36 + 81 = c2
b2 = 45 117 = c2
Square root b squared equals square root 45. Square root 117 equals c squared.
b ≈ 6.71 10.82 ≈ c
Is either of them correct? Explain your reasoning. (5 points)