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Triangle Similarity

"There are four triangle congruence shortcuts: SSS, SAS, ASA, and AAS. We have triangle similarity if (1) two pairs of angles are congruent (AA) (2) two pairs of sides are proportional and the includ ...

Triangle Side and Angle Inequalities

"In any triangle, the largest angle is opposite the largest side (the opposite side of an angle is the side that does not form the angle). The shortest angle is opposite the shortest side. Therefore, ...

Hypotenuse Leg

"In right triangles, if two legs are congruent and if the two hypotenuses are congruent, then the triangles are congruent. This is known as the hypotenuse leg theorem. Note that this is the SSA shortc ...

The Angle Between Vectors

"The vector formula to find the angle between vectors is a useful formula to memorize. This formula uses the dot product, magnitude and cosine to give us the angle between vectors. We can use this for ...

The Angle Between Planes

"We can use knowledge of how to find the angle between vectors to help us find the angle between planes. We can use the dot product to find the angle between planes, or determine whether or not the pl ...

SSS and SAS

"When two triangles are congruent, all three pairs of corresponding sides are congruent and all three pairs of corresponding angles are congruent. If all three pairs of corresponding sides are congru ...

Secants

"A secant is a line, ray, or line segment that intersects a circle in two places. Three points are covered: (1) secants that intersect in a circle which divide each other proportionally, (2) the angl ...

Radii to Tangents

"When a radius is drawn to a point of tangency, the angle formed is always a right (90 degree) angle. This fact is commonly applied in problems with two tangent segments drawn to a circle from a point ...

Constructing an Angle

"When constructing an angle, first swing an arc from the vertex of your angle. Then, swing a congruent arc from the new vertex. Return to the original angle; the drawn arc intersected the sides of the ...

Construct an Angle Bisector

"An angle is formed by two rays with a common endpoint. The angle bisector is a ray or line segment that bisects the angle, creating two congruent angles. To construct an angle bisector you need a c ...

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