HL theorem
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two triangles are congruent
The HL theorem, also known as Hypotenuse-Leg theorem, is a theorem in geometry that outlines a condition under which two right triangles are congruent to each other. According to the HL theorem, if the hypotenuse and a leg of a right-angled triangle are equal to the hypotenuse and leg of another right-angled triangle, then the two triangles are congruent.
In simpler terms, if the hypotenuse and a leg of one right triangle are equal to the hypotenuse and a corresponding leg of another right triangle, then the two triangles are congruent. This can be expressed mathematically as follows:
If in right-angled triangles, ΔABC and ΔPQR, AB = PQ and BC = QR, then the triangles are congruent if and only if AC = PR.
The HL theorem is a special case of the more general SSS (Side-Side-Side) congruence theorem, which states that if three sides of one triangle are equal to three corresponding sides of another triangle, they are congruent.
The HL theorem is important in geometry because it provides a way to determine if two right triangles are congruent without the use of angles. This is helpful in situations where angle measurements may be difficult to obtain or unreliable.
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