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Transcript
Chapter 1: Vertical Angle Theorem: Vertical angles are congruent. Congruent Supplements Theorem: If two angles are supplements of congruent angles (or to the same angle), then the two angles are congruent. Congruent Complement Theorem: If two angles are complements of congruent angles (or to the same angle), then the two angles are congruent. Summary of important Algebra Properties: Reflexive: Something is congruent to itself. Symmetric Property: Congruence is the same forward and backward Transitive Property: Links two equations into one. Chapter 2: Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180°. Exterior Angle Theorem: The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. Corollary: The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles. Polygon Interior Angle-Sum Theorem: The sum of the measures of the interior angles of an n-gon is (n – 2)×180. Polygon Exterior Angle-Sum Theorem: The sum of the measures of the exterior angles of a polygon, one at each vertex, is 180°. Theorem: Two lines parallel to a third line are parallel to each other. Theorem: In a plane, two lines perpendicular to a third line are parallel to each other. Chapter 4: Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Corollary to the Isosceles Triangle Theorem: If a triangle is equilateral, then it is equiangular. Vertex Angle Bisector Theorem: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Converse of the Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite them are congruent. Corollary to the Converse of the Isosceles Triangle Theorem: If a triangle is equiangular, then it is equilateral. Theorem: If a triangle is a right triangle, then the acute angles are complementary. Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. Theorem: All right angles are congruent. Theorem: If two angles are congruent and supplementary, then each is a right angle. Triangle Midsegment Theorem: If a segment joins the midpoints of any two sides of a triangle, then the segment is parallel to the third side and half its length. Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Theorem: If two sides of a triangle are not congruent, then the larger angle lies opposite the larger side. Theorem: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle. Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Converse of the Perpendicular Bisector Theorem: If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. Angle Bisector Theorem: If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. Converse of the Angle Bisector Theorem: If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the angle bisector. Theorem: The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. Theorem: The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides. Theorem: The lines that contain the altitudes of a triangle are concurrent. Theorem: The medians of a triangle are concurrent.