Proving Right Triangles/Pythagorean Theorem

Can a triangle with sides 8, 15, and 17 be a right triangle?

• Yes, because 8² + 15² = 17².

• No, because the sides do not satisfy the Pythagorean theorem.

• Yes, but only if the triangle is isosceles.

• No, because the longest side must be the hypotenuse.

Do the segment lengths 15, 12, and 9 form a right triangle?

• Yes, they form a right triangle.

• No, they do not form a right triangle.

• They form an acute triangle.

• They form an obtuse triangle.

How do you determine if a triangle is a right triangle using side lengths?

• Check if a² + b² = c², where c is the longest side.

• Check if all sides are equal in length.

• Check if the sum of the two shorter sides is greater than the longest side.

• Check if one angle measures 90 degrees.

What is the significance of the right angle in a right triangle?

• It indicates that the triangle can be analyzed using the Pythagorean Theorem.

• It shows that the triangle is equilateral.

• It determines the area of the triangle.

• It indicates that the triangle has two equal sides.

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

• Yes, it is a right triangle because 3² + 4² = 5².

• No, it is not a right triangle because the sides do not satisfy the Pythagorean theorem.

• Yes, it is an obtuse triangle.

• No, it is a scalene triangle.

What is the hypotenuse in a right triangle?

• The shortest side of the triangle.

• The longest side opposite the right angle.

• The side adjacent to the right angle.

• The side opposite the smallest angle.

If a = 2.1, b = 7.2, c = 7.5, is this a right triangle?

• Yes, it is a right triangle.

• No, it is not a right triangle.

• It could be a right triangle depending on the angles.

• The sides do not form a triangle.

What is the Law of Cosines?

• A mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles.

• A theorem that states the sum of the angles in a triangle is 180 degrees.

• A rule that defines the relationship between the sides of a triangle and its area.

• A principle that describes the behavior of parallel lines in geometry.

What is the Pythagorean Theorem?

• In a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c² = a² + b².

• The sum of the angles in a triangle is always 180 degrees.

• The area of a circle is calculated using the formula A = πr².

• In a right triangle, the length of the hypotenuse is always greater than the lengths of the other two sides.

What is a right triangle?

• A triangle with all angles measuring less than 90 degrees.

• A triangle that has one angle measuring 90 degrees.

• A triangle with two equal sides and one angle measuring 60 degrees.

• A triangle that has no equal sides and one angle measuring 45 degrees.