Right Triangles

Hypotenuse

The longest side of a right triangle

The pythagorean theorem

a²+b² = c²

Converse of the pythagorean theorem

If a,b, and c are side lengths of a triangle and a²+b² = c² =, then the triangle is a right triangle

Pythagorean triple

When 3 whole numbers satisfy a²+b² = c²

HL congruence theorem

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg length of another, then the right triangles are congruent. (SSS)

LL Theorem

If the legs of one right triangle are congruent to another’s, then the triangles are congruent.(SSS and SAS)

HA Theorem

If the hypotenuse and an acute angle of one right triangle are congruent to another’s, then the triangles are congruent(AAS)

LA Theorem

IF the leg & an acute angle of one right triangle are congruent to another’s, then the triangles are congruent. (ASA & AAS)

Perpendicular Bisector Theorem

If a point is on the perpendicular Bisector of a segment, then it is equidistant from the end points of the segment

Converse of the Perpendicular Bisector Theorem

If a point is equidistant from the endpoints of a triangle, then it lies on the perpendicular bisector

Angle bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle

Right Triangle Similarity Theorem

If the altitude is drawn from the vertex of the right triangle to the triangle’s hypotenuse, then the two right triangles formed are similar to the original triangle & each other.

the side lengths of a 45,45,90 triangles

the legs are equal, and the hypotenuse is the length of the legs times square root of 2

the side lengths of a 30-60-90 triangle

The hypotenuse is 2x the smallest leg, while the longer leg is the square root of 3 by the smallest leg