GEOMETRY FUNDAMENTALS - UNIT 11 Essays - Geometry, Quadrilaterals

GEOMETRY FUNDAMENTALS - UNIT 11 REVIEW CONGRUENT TRIANGLES AND QUADRILATERALS Altitude of a triangleA segment from a vertex perpendicular to the opposite side.Congruent trianglesTwo triangles in which the six parts of one are equal to the corresponding six parts of the other.Included angleThe angle formed by two sides of a triangle. The angle is between, and formed by, the two sides.Included sideThe side of a triangle that is the common side of two angles. The side is between the two angles.Isosceles trapezoidA trapezoid with legs of the same length.Isosceles triangleA triangle with at least two sides equal.Median of a trapezoidThe segment connecting the midpoint of the legs.Median of a triangleA segment from a vertex to the midpoint of the opposite side.ParallelogramA quadrilateral with both pairs of opposite sides parallel.RectangleA parallelogram with four right angles.RhombusA parallelogram with all sides equal.SquareA rectangle with all sides equal.TrapezoidA quadrilateral with exactly one pair of sides parallel. P11SSS:If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.P12SAS:If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.P13ASA:If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.P14HL:If the hypotenuse and a leg of one right triangle are equal to the hypotenuse and leg of another right triangle, then the triangles are congruent. Theorem 4-14, included among the following theorems, is the theorem that allows triangle postulates and theorems to be applied to parallelograms. Be sure you can prove each theorem reviewed. 4-1If two angles and a not-included side of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent. (AAS)4-2:If two legs of one right triangle are equal to two legs of another right triangle, then the triangles are congruent. (LL)4-3:If the hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent. (HA)4-4:If a leg and an acute angle of one right triangle are equal to a leg and an acute angle of another right triangle, then the triangles are congruent. (LA)4-5:The altitude to the base of an isosceles triangle bisects the base.4-6:The base angles of isosceles triangles are equal.4-7:The altitude to the base of an isosceles triangle bisects the vertex angle of the triangle.4-8:If two angles of a triangle are equal, then the sides opposite them are equal.4-9:If two sides of a triangle are not equal, then the angle opposite the longer side is the larger angle.4-10:If two angles of a triangle are not equal, then the side opposite the larger angle is the longer side.4-11:The sum of the lengths of any two sides of a triangle is greater than the length of the third side.4-12:If two sides of one triangle are equal to two sides of another triangle but the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.4-13:If two sides of one triangle are equal to two sides of another triangle but the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first is larger than the included angle of the second.MORE THEOREMS4-14:If a diagonal is drawn in a parallelogram, then two congruent triangles are formed.Corollary 1:Opposite angles of a parallelogram are equalCorollary 2:Opposite sides of a parallelogram are equal.Corollary 3:Two parallel lines are equidistant apart throughout.4-15:The diagonals of a parallelogram bisect each other.4-16:If two sides of a quadrilateral are equal and parallel, then the quadrilateral is a parallelogram.4-17:If both pairs of opposite sides of a quadrilateral are equal, then the quadrilateral is a parallelogram.4-18:If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.4-19:If the midpoints of two sides of a triangle are connected, the segment is parallel to the third side and measures half the length of the third side4-20:The diagonals of a rectangle are equal.4-21:The diagonals of a