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TRIANGLE THEOREMS
| Exterior Angle of a Triangle: | The measure of an exterior angle of a triangle is equal to the sum of the two non-supplementary angles. |
| Isosceles Triangle Theorem: | If two sides of a triangle are congruent, then the angles opposite those sides are congruent. |
| Triangle Inequality Theorem: | The sum of any two sides of a triangle must be strictly larger than the third side. |
| Hinge Theorem: | If two sides of triangle A are congruent to two sides of triangle B and the angle between the sides of A is greater than the angle of B, then the third side of A is larger than the third side of B. |
| Acute Angles of a Right Triangle: | The acute angles of a right triangle are complementary. |
| LL Theorem: | If the legs of one right triangle are congruent to the legs of another right triangle, then the triangles are congruent. |
| HA Theorem: | If the hypotenuse and acute angle of one right triangle is congruent to the corresponding parts of another right triangle, then the triangles are congruent. |
| LA Theorem: | If one leg and acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. |
| HL Postulate: | If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. |
| A Chord Perpendicular to a Diameter: | In a circle, if a chord is perpendicular to a diameter, then the diameter bisects the chord and the included arc. |
| Intersecting Chords: |
If two chords intersect in a circle, then the products of the measures of the segments are equal. |
| Inscribed Angle: | If an angle is inscribed in a circle, then the measure of the angle is one-half the measure of the intercepted arc. |
| Inscribed Angle Containing Diameter: | If an inscribed angle of a circle intercepts a diameter (hence, intercepts a semi-circle), then the angle is a right angle. |
| Inscribed Quadrilateral: | If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. |
| Radius Perpendicular to a Tangent: | If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. |
| Two Intersecting Tangent Segments: | If two segments from the same exterior point are tangent to a circle, then the segments are congruent. |
| A Secant Intersecting a Tangent at Point of Tangency: | If a secant and a tangent intersect at the point of tangency, then the measure of the angle formed is one-half the measure of its intercepted arc. |
| Two Intersecting Secant Segments: | If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the arcs intercepted by the angle and its vertical angle. |
| A Secant Intersecting a Tangent at Exterior Point: | If a tangent segment and a secant segment are drawn to a circle from an exterior point, the square of the measure of the tangent segment is equal to the product of the measure of the secant segment and its external segment. |
| Sides and Angles of a Parallelogram: | In a parallelogram, opposite sides and opposite angles are congruent. Consecutive angles are supplementary. |
| Diagonals of a Parallelogram: | In a parallelogram, the diagonals bisect each other. |
| Diagonals of a Rectangle: | Diagonals of a rectangle are congruent. |
| Properties of a Rhombus: | The diagonals of a rhombus are perpendicular to each other. Each diagonal of a rhombus bisects a pair of opposite angles. |
| Properties of a Trapezoid: | In an isosceles trapezoid, both pairs of base angles are congruent. The diagonals of an isosceles trapezoid are congruent. The median of a trapezoid is parallel to the bases and its measure is one-half the sum of the measure of the bases. |
LINES, ANGLES AND A POLYGON THEOREMS
| A Point on a Perpendicular Bisector: | If a point lies on the perpendicular bisector of a segment, then the point is equidistant to the endpoints of the segment. |
| A Point on an Angle Bisector: | If a point lies on the bisector of an angle, then the point is equidistant to the sides of the angle. |
| Alternate Exterior Angles: | If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. |
| Alternate Interior and Consecutive Angles: | If two parallel lines are cut by a transversal, then alternate interior angles are congruent and consecutive angles are supplementary. |
| Exterior Angles of Polygons: | The sum of all the exterior angles of any convex polygon will be 360°. |