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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 ...

Trigonometric Identities

"Identities are equations true for any value of the variable. Since a right triangle drawn in the unit circle has a hypotenuse of length 1, we define the trigonometric identies x=cos(theta) and y=sin( ...

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 Altitude

"Altitudes are defined as perpendicular line segments from the vertex to the line containing the opposite side. In each triangle, there are three triangle altitudes, one from each vertex. In an acute ...

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 ...

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 ...

Proportional Segments

"When a line is drawn parallel to one side in a triangle, two similar triangles are formed because corresponding angles yield the AA similarity shortcut. Because the triangles are similar, the segment ...

Pascal's Triangle

"Pascal's triangle is a geometric arrangement of the binomial coefficients in the shape of a triangle. In Pascal's triangle, each number in the triangle is the sum of the two digits directly above it. ...

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