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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 Mid segment

"A triangle mid segment is a line segment whose endpoints are the midpoints of a triangle. The triangle mid segment is parallel to the third side (the side that does not contain an endpoint). Also, ...

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 ...

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 ...

Trapezoid Midsegment

"A midsegment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid. A trapezoid midsegment is parallel to the set of parallel lines in a trapezoid ...

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 ...

Surface Area of a Pyramid

"Surface area is a two-dimensional property of a three-dimensional figure. Pyramids have polygonal bases and triangular faces, which are congruent if the base is regular. To find the total surface a ...

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