# Question: Is The Hypotenuse Always The Longest Side?

## Can the hypotenuse be equal to a leg?

The legs of this triangle are each of length 1 unit as they are both original sides of the unit square.

In other words, in every 45-45-90 triangle, the lengths of the two legs are always equal, and the ratio of the length of the hypotenuse to the length of a leg is always square root 2 to 1..

## What is a leg in Pythagorean Theorem?

The other two (shorter) sides are called legs. The Pythagorean Theorem states that if you add the squares of the lengths of the two legs of a right triangle you will always obtain the square of the length of the hypotenuse.

## What does Pythagoras theorem mean?

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

## What is the rule for sides of a triangle?

According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side.

## Does 5 12 and 13 make a right triangle?

The best known triple is 3-4-5, with 5-12-13 being the next most recognized. Any triangle composed of sides of lengths that match the Pythagorean triple will be a right triangle. That means our triangle has a 90 degree angle for angle C.

## Why is the hypotenuse always the longest side?

Explanation: In any triangle sides, opposite to congruent angles, are congruent. A side, opposite to a bigger angle, is bigger than a side that lies opposite to a smaller angle. … The largest angle in a right triangle is the right angle, therefore, opposite to it lies the longest side – hypotenuse.

## Can the hypotenuse be the same length as another side?

The hypotenuse is the longest side of a right triangle, so a right triangle can never have a leg equal to the length of any leg of any right triangle. So, the answer is NO. … The Pythagorean theorem is a theorem in Euclidean geometry about right triangles.

## How do you know if it is a right triangle?

A right triangle is a triangle in which one of the angles is a 90∘ angle. The “square” at the vertex of the angle indicates that it is 90 degrees. A triangle can be determined to be a right triangle if the side lengths are known. If the lengths satisfy the Pythagorean Theorem (a2+b2=c2) then it is a right triangle.

## How do you find the missing side of a triangle that is not right?

The law of cosines can be used to find the measure of an angle or a side of a non-right triangle if we know:two sides and the angle between them or.three sides and no angles.

## Do all triangles have a hypotenuse?

Yes, the hypotenuse is always the longest side, but only for right angled triangles. For isosceles triangles, the two equal sides are known as the legs, while in an equilateral triangle all sides are known simply as sides.

## What is the length of the hypotenuse of a right triangle with leg lengths of 5 inches and 12 inches?

Finding the Length of the Hypotenuse In the triangle above, you are given measures for legs a and b: 5 and 12, respectively. You can use the Pythagorean Theorem to find a value for the length of c, the hypotenuse. Using the formula, you find that the length of c, the hypotenuse, is 13.

## How do you find a hypotenuse?

If you are given the length of the shortest leg (opposite the 30-degree angle,) simply multiply the leg length by 2 to find the length of the hypotenuse. … If you are given the length of the longer leg (opposite the 60-degree angle,) multiply that length by 2/Sqrt(3) to find the length of the hypotenuse.

## Do the segments 15 12 and 9 form a right triangle?

Correct answer: By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.

## Is hypotenuse only for right triangles?

In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. … The length of the hypotenuse is the square root of 25, that is, 5.

## Does 4 5 6 make right triangles?

Explanation: For a set of three numbers to be pythagorean, the square of the largest number should be equal to sum of the squares of other two. Hence 4 , 5 and 6 are not pythagorean triple.

## Is Pythagorean theorem only for right triangles?

Pythagoras’ theorem only works for right-angled triangles, so you can use it to test whether a triangle has a right angle or not.

## Which set of sides would make a right triangle?

A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. There are a couple of special types of right triangles, like the 45°-45° right triangles and the 30°-60° right triangle.

## What is the longest side of a right triangle?

hypotenuseThe hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle. The other two sides are called the opposite and adjacent sides.

## What is the hypotenuse leg Theorem?

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

## How do you prove that the hypotenuse is the longest side?

Expert Answer:Given :A right angledtriangle ABC, B = 90oTo Prove:Hypotenuse AC in the longest side.(i) AC > AB(ii)AC > BC.Proof: Now in ABC.ABC = 90oBut CAB + BCA + CBA = 180oThus BCA < 90o and CAB < 90o(Side opposite to greater angle is larger)More items...•

## Is C always the hypotenuse?

The Pythagorean Theorem is a formula that gives a relationship between the sides of a right triangle The Pythagorean Theorem only applies to RIGHT triangles. … NOTE: The side “c” is always the side opposite the right angle. Side “c” is called the hypotenuse. The sides adjacent to the right angle are named “a” and “b”.