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Why SSA and AAA Don't Work as Congruence Shortcuts

"Four shortcuts allow students to know two triangles must be congruent: SSS, SAS, ASA, and AAS. Knowing only side-side-angle (SSA) does not work because the unknown side could be located in two differ ...

Using Sine to Calculate the Area of a Triangle

"Using the standard formula for the area of a triangle, we can derive a formula for using sine to calculate the area of a triangle. Using sine to calculate the area of a triangle means that we can fin ...

Triangle Angle Sum

"The sum of the three angles in any triangle sum to 180 degrees. The importance of this fact in Geometry cannot be emphasized enough. The triangle angle sum theorem is used in almost every missing a ...

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 ...

Remote Interior Angles

"If one side of a triangle is extended beyond the vertex, an exterior angle is formed. This exterior angle is supplementary with its adjacent, linear angle. Since the angle sum in a triangle is also 1 ...

Area of Triangles

"The formula for calculating the area of triangles comes from dividing a parallelogram in half, so the area is half of base times height. When finding the area of a triangle, the height is an altitud ...

Area of Regular Polygons

"If radii are drawn from the center of a regular polygon to the vertices, congruent isosceles triangles are formed. Using the apothem as the height and the polygon side as the base, the area of each ...

Area of a Segment

"The area of a segment in a circle is found by first calculating the area of the sector formed by the two radii and then subtracting the area of the triangle formed by the two radii and chord (or seca ...

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