Triangle Inequality Thereom
The sum of the measures of any two sides of a triangle must be greater than the third side.
Triangle Sum Thereom
The sum of the measures of the interior angles of a triangle is 180 degrees.
Acute Angle Thereom
The acute angles of a right triangle are congruent.
Third Angles Thereom
If two angles of one triangle are congruent to two angles of another triangle then the third angles are congruent.
Exterior Angles Thereom
The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles.
Base Angles Thereom
If two sides of a triangle are congruent, then the angles opposite them are also congruent.
CPCTC
Corresponding Parts of Congruent Triangles are Congruent.
SSS Triangle Congruency
If three sides of one triangle are congruent to the corresponding three sides of another triangle then the triangles are congruent.
Hypotenuse Leg Triangle Congruency
If the leg and hypotenuse of one right triangle is congruent to the corresponding hypotenuse and leg of another right triangle then the triangles are congruent.
SAS Triangle Congruency
If two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle then the two triangles are congruent.
ASA Triangle Congruency
If two angles and the included side of one triangle are congruent to the corresponding two angles and the included side of another triangle then the two triangles are congruent.
AAS Triangle Congruency
If two angles and the non-included side of one triangle are congruent to the corresponding two angles and the non-included side of another triangle then the two triangles are congruent.
Angle Bisector
A ray, line, or plane that divides an angle into two congruent angles.
Alternate Exterior Angles
Angles that lie on the exterior of two lines but on opposite sides of the transversal.
Alternate Interior Angles
Angles that lie on the interior of two lines but on opposite sides of the transversal.
Consecutive Interior Angles
Angles that lie on the interior of two lines and on same sides of the transversal.
Corresponding Angles
Angles that lie on the same position on the lines and the transversal.
Linear Pair
A pair of adjacent angles whose non-adjacent sides form opposite rays.
Vertical Angles
A pair of non-adjacent angles whose sides form opposite rays.
Perpendicular Lines
Two lines that intersect to form a right angle.
Straight Angle
An angle whose measure equals 180 degrees.
theorem 6-1
opposite sides of a parallelogram are ≅.
theorem 6-2
opposite ∠'s of a parallelogram are ≅.
theorem 6-3
consecutive ∠'s in a parallelogram are supplementary (180 degrees)
theorem 6-4
The diagonals of a parallelogram bisect each other
theorem 6-5
If both pairs of opposite sides of a quadrilateral are ≅, then the quadrilateral is a parallelogram.
theorem 6-6
If both pairs of opposite ∠'s of a quadrilateral are ≅, then the quadrilateral is a parallelogram.
theorem 6-7
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
theorem 6-8
If 1 pair of opposite sides of a quadrilateral is both parallel and ≅, then the quadrilateral is a parallelogram.
theorem 6-9
If a parallelogram is a rectangle, then its diagonals are ≅.
theorem 6-10
If the diagonals of a parallelogram are ≅, then the parallelogram is a rectangle.
theorem 6-11
The diagonals of a rhombus are ⊥.
theorem 6-12
If the diagonals of a parallelogram are ⊥, then the parallelogram is a rhombus.
theorem 6-13
If the diagonals of a rhombus bisects a pair of opposite ∠'s.
Theorem 6-14
Both pairs of base ∠'s of an isosceles trapezoid are ≅.
theorem 6-15
The diagonals of an isosceles trapezoid are ≅
theorem 6-16
The median of a trapezoid is parallel to the bases, and it's measure is ½ the sum of the measures of the bases.
If a quadrilateral is a rectangle then...
1. opposite sides are ≅ and parallel.2. opposite sides are ≅.3. consecutive ∠'s are supplementary (180°)4. diagonals are ≅ and bisect each other.5. all 4 ∠'s are right angles (90°)