Quiz: Angles and the Pythagorean Theorem
Part 1: Multiple Choice Questions
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Angles of Triangles
A triangle has one angle measuring 60 degrees and another angle measuring 80 degrees. What is the measure of the third angle?
A) 40 degrees
B) 60 degrees
C) 70 degrees
D) 80 degrees -
Angles and Parallel Lines
Which of the following pairs of angles are corresponding angles?
A) Angles on opposite sides of a transversal line
B) Angles in the same position on parallel lines
C) The interior angles of a triangle
D) None of the above -
Pythagorean Theorem
In a right triangle, if one leg is 6 units long and the other leg is 8 units long, what is the length of the hypotenuse?
A) 10 units
B) 12 units
C) 14 units
D) 16 units -
Distance and the Pythagorean Theorem
What is the distance between the points (3, 4) and (7, 1) in the Cartesian plane?
A) 5 units
B) √13 units
C) √20 units
D) √25 units
Part 2: Short Answer Questions
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Use the Pythagorean Theorem
A ladder leans against a wall, forming a right triangle with the ground. If the base of the ladder is 4 feet away from the wall and the top reaches 3 feet on the wall, what is the length of the ladder? -
The Pythagorean Theorem in Three Dimensions
Find the distance between the points (1, 2, 3) and (4, 6, 8) in three-dimensional space using the Pythagorean theorem.
Part 3: Word Problems
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Angles of Triangles
A triangle has angles that are in a ratio of 2:3:4. What are the measures of each angle? -
Angles and Parallel Lines
If two parallel lines are cut by a transversal, and one of the alternate interior angles measures 120 degrees, what is the measure of the corresponding angle?
Answers:
- C) 70 degrees
- B) Angles in the same position on parallel lines
- A) 10 units
- A) 5 units
- Length of the ladder = √(4² + 3²) = √(16 + 9) = √25 = 5 feet.
- Distance = √((4-1)² + (6-2)² + (8-3)²) = √(3² + 4² + 5²) = √(9 + 16 + 25) = √50 = 5√2 units.
- The angles are 40 degrees, 60 degrees, and 80 degrees.
- The corresponding angle is also 120 degrees.
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