32 Questions
What is the longest side in a right-angled triangle?
The side opposite the right angle
What is the condition for a triangle to be acute-angled?
All angles are less than 90 degrees
What is the formula to find the length of the hypotenuse in a right-angled triangle?
c = √(a^2 + b^2)
Which of the following triangles satisfies the condition a^2 + b^2 > c^2?
Acute-angled triangle
What is the first step in using the Pythagorean theorem to find an unknown side?
Identify the sides
What is the converse of the Pythagorean theorem?
If c^2 = a^2 + b^2, then the triangle is right-angled
Which of the following is a key point about the Pythagorean theorem?
It only applies to right-angled triangles
What can be concluded about a triangle if a^2 + b^2 < c^2?
The triangle is obtuse-angled
What can be concluded about a triangle if it satisfies the condition a^2 + b^2 = c^2?
It is a right-angled triangle.
In which type of triangle does the relationship a^2 + b^2 > c^2 hold?
Acute-angled triangle.
What is the purpose of the Pythagorean theorem?
To find the length of the hypotenuse in a right-angled triangle.
If a triangle satisfies the condition c^2 = a^2 + b^2, what can be concluded about the triangle?
It is a right-angled triangle.
What is the name of the theorem that states a^2 + b^2 = c^2 in a right-angled triangle?
Pythagorean theorem.
What is the relationship between the length of the hypotenuse and the lengths of the other two sides in a right-angled triangle?
The square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In which type of triangle is the hypotenuse always the longest side?
Right-angled triangle.
What is the formula to find a side in a right-angled triangle, given the lengths of the other two sides?
a = √(c^2 - b^2).
If a triangle has sides of length 3, 4, and x, which of the following can be concluded about the triangle?
The triangle is right-angled and x is the length of the hypotenuse.
Which of the following is true about the relationship between the sides of an obtuse-angled triangle?
a^2 + b^2 < c^2
What can be concluded about a triangle if a^2 + b^2 = 2c^2?
The triangle is isosceles.
If a triangle has sides of length 5, 12, and x, which of the following is true?
The triangle is right-angled and x is the length of the hypotenuse.
Which of the following is a necessary condition for a triangle to be right-angled?
The sum of the squares of two sides is equal to the square of the third side.
What can be concluded about a triangle if a^2 - b^2 = c^2?
The triangle is isosceles.
If a triangle has sides of length 7, 24, and x, which of the following can be concluded about the triangle?
The triangle is right-angled and x is the length of the hypotenuse.
Which of the following is a sufficient condition for a triangle to be acute-angled?
a^2 + b^2 > c^2
If a triangle has sides of length 3, 5, and x, which of the following is true?
The triangle is right-angled.
What is the relationship between the length of the hypotenuse and the lengths of the other two sides in a right-angled triangle?
The square of the hypotenuse is equal to the sum of the squares of the other two sides.
If a triangle satisfies the condition a^2 + b^2 > c^2, what can be concluded about the triangle?
The triangle is acute-angled.
What is the purpose of the converse of the Pythagorean theorem?
To determine if a triangle is right-angled.
If a triangle has sides of length 7, 24, and 25, which of the following can be concluded about the triangle?
The triangle is right-angled.
What is the formula to find the length of a side in a right-angled triangle, given the lengths of the other two sides?
a = sqrt(c^2 - b^2)
If a triangle satisfies the condition a^2 + b^2 < c^2, what can be concluded about the triangle?
The triangle is obtuse-angled.
In which type of triangle is the Pythagorean theorem not applicable?
Obtuse-angled triangle.
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