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Theorem Toolkit Use this toolkit to add to or correct your own toolkits. You may NOT print this out and use it on a test!! A quadrilateral is a four-­‐sided polygon. The sum of the interior angles is 360°. Parallelograms Kites • Opposite sides • Have two pairs of are parallel and adjacent congruent congruent. sides. • Opposite angles • One diagonal bisects are congruent. the other and also bisects the opposite • Angles that are not opposite are angles. supplementary. • The diagonals are • The diagonals bisect each other. perpendicular. • Have one set of opposite congruent angles. Rhombi Rectangles • All sides are • Quadrilaterals with congruent. four right angles. • Opposite sides are • All rectangles are parallel. also parallelograms (so opposite sides are parallel). • The diagonals bisect each other. • The diagonals bisect each other. • The diagonals are • The diagonals are congruent to each other. perpendicular. • Opposite sides are congruent. • Consecutive angles are supplementary. • Diagonals bisect the angles they go through. Trapezoids Squares • Have one set of • Opposite sides are parallel sides. parallel. • All sides are congruent. • The diagonals bisect Isosceles Trapezoids each other. • Have one set of • Have four 90° angles. parallel sides. • Diagonals are congruent. • Have congruent legs • Diagonals are perpendicular. (non-­‐parallel sides) • Have congruent base angles. • Have congruent diagonals. Triangle Midsegment Theorem A midsegment of a triangle is a segment that connects the midpoints of any two sides of a triangle. Every triangle has three midsegments, as shown below. A midsegment between two sides of a triangle is half the length of and parallel to the third side of the !
triangle. For example, in ΔABC above, 𝐷𝐸 is a midsegment, 𝐷𝐸 ∥ 𝐴𝐶, and 𝐷𝐸 = ! 𝐴𝐶.