To calculate the hypotenuse of a right-angled triangle we use the Pythagoraean Theorem: Hypotenuse = √(Base 2 + Perpendicular 2). What is the Formula to Calculate the Hypotenuse of a Right-Angled Triangle? The hypotenuse is the longest side of the triangle, while the other two legs are always shorter in length. In a right-angled triangle, the side opposite to the right angle is called the hypotenuse and the two other adjacent sides are called its legs. Right Angled Triangle Constructions(RHS)įAQs on Hypotenuse Leg Theorem What is the Difference Between the Legs and the Hypotenuse of a Triangle?.Related Articles on Hypotenuse Leg TheoremĬheck out the following pages related to the hypotenuse leg theorem. The only difference is that SAS needs two sides and the included angle, whereas, in the HL theorem, the known angle is the right angle, which is not the included angle between the hypotenuse and the leg. The HL Congruence rule is similar to the SAS (Side-Angle-Side) postulate.According to the HL Congruence rule, the hypotenuse and one leg are the elements that are used to test the congruence of triangles.This is represented as: Hypotenuse² = Base² + Perpendicular². The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides (base and perpendicular).We also know that the angles BAD and CAD are equal.(AD bisects BC, which makes BD equal to CD).
We know that angles B and C are equal (Isosceles Triangle Property). Therefore, a hypotenuse and a leg pair in two right triangles, are satisfying the definition of the HL theorem. AD = AD because they are common in both the triangles. AB and AC are the respective hypotenuses of these triangles, and we know they are equal to each other. Proof:ĪD, being an altitude is perpendicular to BC and forms ADB and ADC as right-angled triangles. Given: Here, ABC is an isosceles triangle, AB = AC, and AD is perpendicular to BC. Observe the following isosceles triangle ABC in which side AB = AC and AD is perpendicular to BC. In the event of a complaint from a sale where finance was the payment method we will work to resolve this in-house with you and in line with the Financial Conduct Authority () & Financial Ombudsman Service () requirements.The proof of the hypotenuse leg theorem shows how a given set of right triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.
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