Download Proof Toolbox - Middletown Public Schools

ADVANCED GEOMETRY: OUR PROOF TOOLBOX
(Unit 3)
Definitions that can be used to justify steps in a proof:
A regular polygon is a polygon for which all sides are congruent and all angles are
congruent.
Alternate Interior Angles – a pair of angles formed by two lines and a transversal. The
angles must lie in the interior of the figure, must lie on alternate sides of the transversal,
and must have different vertices.
Alternate Exterior Angles – a pair of angles formed by two lines and a transversal. The
angles must lie in the exterior of the figure, must lie on alternate sides of the transversal,
and must have different vertices.
Corresponding Angles - a pair of angles formed by two lines and a transversal. One
angle must lie in the interior of the figure, and the other must lie in the exterior. The
angles must lie on the same side of the transversal but have different vertices.
A parallelogram is a quadrilateral with opposite sides parallel.
A rectangle is a parallelogram with four right angles.
A rhombus is a parallelogram with four sides of equal length.
A kite is a quadrilateral with two pairs of congruent adjacent sides.
A trapezoid is a quadrilateral with exactly one pair of parallel sides (per our text).
An isosceles trapezoid is a trapezoid in which the nonparallel sides are congruent. Note:
The nonparallel sides are called the legs of the trapezoid. The parallel sides are called the
bases of the trapezoid.
Theorems that can be used as justification for steps in a proof:
// lines  alt. int . s 
// lines  alt. ext. s 
// lines  corr. s 
alt . int . s   // lines
alt . ext. s   // lines
corr. s   // lines
Opposite sides of a parallelogram are congruent.
Opposite angles in a parallelogram are congruent.
Diagonals of a parallelogram bisect each other.
The diagonals of a rectangle are congruent.
The diagonals of a rhombus bisect the angles of the rhombus.
The diagonals of a rhombus intersect at right angles.
We can also use algebra, a given statement, or a marked
diagram to justify a step in a proof,
Formulas that we have justified:
Interior angle sum in a polygon with n sides: S  180(n  2)
Exterior angle sum (one at each vertex) in a polygon with n sides: E  360