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Download Math 11P Geometry Reasons for Proofs FULL THEOREM
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Transcript
Math 11P Geometry Reasons for Proofs FULL THEOREM SHORTHAND ANGLES Complementary angles add to 90 Supplementary angles add to 180 Perpendicular lines for two 90 angles A straight line forms a 180 angle Angles at a point add to 360 Vertically opposite angles are equal Comp s Supp s Def s on a line s at a point Vert opp s PARALLEL LINES AND TRANSVERSALS Corresponding angles are equal Alternate interior angles are equal Interior angles on the same side of the transversal are supplementary Corr s Alt int s Int s TRIANGLE PROPERTIES Angles in a triangle add to 180 Angles opposite equal sides of an isosceles triangle are equal Sides opposite equal angles of an isosceles triangle are equal If all angles of a triangle are 60, then all the sides are equal If all sides of a triangle are equal, then each angle is 60 If one angle of a triangle is 90, then the sides are related by s in a Isos Isos Equil Equil Pythag a2 b2 c2 CONGRUENT TRIANGLES If each side of one triangle is congruent to a side of a second triangle, then the triangles are congruent If two sides and the angle between them from one triangle are congruent to two sides and the angle between them for a second triangle, then the triangles are congruent If two angles and the side contained between them from one triangle are congruent to two angles and the side contained between them for a second triangle, then the triangles are congruent If two angles form one triangle are equal to two angles from another triangle, then the third angles form each triangle must also be equal If 2 sides of a right triangle are equal to 2 corresponding sides of a second right triangle, then the third sides of each triangle must be equal. Corresponding Parts of Congruent Triangles are Congruent If M is the midpoint of AB, then AM=BM If line AB divides an angle into 2 equal parts, it is called the angle bisector If a line is perpendicular to a line segment and divides it into 2 equal parts, it is called the perpendicular bisector SSS SAS ASA 3rd s in s Pythag CPCTC Def MP Def bisector Def bisector FULL THEOREM SHORTHAND CIRCLE PROPERTIES (MATH 11) The perpendicular bisector of a chord passes through the center of the circle A line through the center of a circle which bisects a chord is perpendicular to the chord A line through the center of a circle which is perpendicular to a chord bisects the chord Inscribed angles which end on the same chord or equal chords are equal Central angles are double inscribed angles which end on the same chord or equal chords Inscribed angles and half central angles which end on the same chord or equal chords Angles inscribed on a semi-circle (or diameter) measure 90 Tangents are perpendicular to radii at the point of tangency The two tangent line segments from an external point to their points of tangency are equal in length Opposite angles of a cyclic quadrilateral are supplementary The angle between a tangent and a chord is equal to the inscribed angle on the opposite side of the chord Chord bisector theorem Chord bisector theorem Chord bisector theorem Ins s = Central s = 2x Ins s Ins s = ½ Central s s ins on a semi-circle Tan radii Tangents from an external pt Opp s of cyclic quad Tangent-chord thm
