Pythagorean Theorem
What is the Pythagorean Theorem formula?
Answer: a2 + b2 = c2
What does the Triangle Inequality Theorem state?
Answer: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
What are supplementary angles?
Answer: Two angles that add up to 180°.
How do you find the area of a rectangle?
Answer: Length × Width.
What is a linear equation?
Answer: An equation that makes a straight line when graphed.
If one leg of a right triangle is 3 units and the other leg is 4 units, what is the length of the hypotenuse?
Answer: 5 units
Can a triangle be formed with side lengths of 5, 7, and 12? Explain.
Answer: No, because 5 + 7 is not greater than 12.
If two angles are complementary, what is the sum of their measures?
Answer: 90°.
What is the formula for the area of a triangle?
Answer: 1/2 × Base × Height
Solve the equation 2x + 3 = 11.
Answer: x = 4
A ladder leans against a wall, forming a right triangle with the ground. If the ladder is 10 feet long and is positioned 6 feet away from the wall, how high does the ladder reach on the wall?
Answer: 8 feet
What is the converse of the Pythagorean Theorem?
Answer: If the square of the length of one side equals the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
What are vertical angles?
Answer: Angles opposite each other when two lines intersect; they are congruent.
If a polygon can be decomposed into triangles, how do you find the sum of its interior angles?
Answer: Use the formula (n−2) × 180°, where n is the number of sides.
How do you graph a linear inequality?
Answer: Graph the boundary line and shade the region that satisfies the inequality.
Calculate the distance between the points (1, 2) and (4, 6) using the Pythagorean Theorem.
Answer: 5 units
If a triangle has angles measuring 30°, 60°, and 90°, what type of triangle is it?
Answer: It is a right triangle.
How do you find the measure of an interior angle of a triangle?
Answer: The sum of the interior angles of a triangle is always 180°.
Calculate the area of a triangle with a base of 10 units and a height of 5 units.
Answer: 25 square units.
Solve the inequality -3x - 15 < 45.
Answer: x > -20
Explain how the Pythagorean Theorem can be applied to real-world problems.
Answer: It can be used to determine distances, heights, and other measurements involving right triangles.
Describe how to use the Triangle Inequality Theorem to determine if a triangle can be formed using sides of lengths 8, 15, and 20.
Answer: Check if 8 + 15 > 20, 8 + 20 > 15, and 15 + 20 > 8; since 8 + 15 is not greater than 20, a triangle cannot be formed.
If one angle of a triangle is 70° and another is 50°, what is the measure of the third angle?
Answer: 60° (because 180° - 70° - 50° = 60°).
Explain how to find the area of a composite figure made up of a rectangle and a triangle.
Answer: Find the area of both shapes separately and then add them together.
Explain how to solve a multi-step equation with variables on both sides, such as 2x + 3 = x + 7.
Answer: Subtract x from both sides to get
x + 3 = 7, then subtract 3 from both sides to find x = 4.