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Geom 1-2 (E) Quarter 02 Exam OVERVIEW Name: _______________________________________ Period: ____ 1.) Midpoints, bisectors, trisectors B is the midpoint of AC . If AC 2x 1 and BC 5x 12 , find the value of x and the measure of AB . 2.) Perpendicular FO OX . Find If mYOX . 3.) Complementary and supplementary angles The supplement of an angle is 6 times the measure of the complement of the same angle. Find the angle, the complement, and the supplement. 4.) Ratios Two complementary angles are in a ratio of 2:3. Find the supplement of the larger of the two angles. 5.) Equilateral and isosceles triangles, sum of angles in a triangle, and the exterior angle theorem PIN is isosceles with base PN . Find the value of y . Proofs Addition and subtraction properties Vertical angles and substitution property Isosceles triangles Congruent triangles (Proper labeling and order) Triangle congruency theorems (SSS, SAS, ASA, AAS, HL) CPCTC Definitions (Reversible) Congruent If two segments or angles are congruent, then they have the same measure. Right Angle If an angle is a right angle, then it has a measure of 900. Straight Angle If an angle is a straight angle, then it has a measure of 1800. Midpoint If a point is a midpoint, then it divides a segment into 2 congruent segments. Segment Bisector If a point, segment, ray, or line bisect a segment, then it divides a segment into 2 congruent segments. Angle Bisector If a segment, ray, or line bisect an angle, then it divides an angle into 2 congruent angles. Segment Trisector If 2 points, segments, rays, or lines trisect a segment, then they divide a segment into 3 congruent segments. Angle Trisector If 2 segments, rays, or lines trisect an angle, then they divide an angle into 3 congruent angles. Complementary If two angles are complementary, then they add to form a right angle or 900. Supplementary If two angles are supplementary, then they add to form a straight angle or 1800. Perpendicular If two segments, rays, or lines are perpendicular, then they intersect to form right angles. Isosceles Triangle If a triangle is isosceles, then at least 2 sides are congruent. Equilateral Triangle If a triangle is equilateral, then all 3 sides are congruent. Right Triangle If a triangle contains one right angle, then it is a right triangle. Median If a segment is a median, then it goes from a vertex of a triangle to the midpoint of the opposite side. Altitude If a segment is an altitude, then it goes from a vertex of a triangle perpendicular to the opposite side (extended) Theorems (Not reversible!) q p is true) If a conditional statement is true, its contrapositive is true. (If p q is true, then If two angles are right angles, then they are congruent. If two angles are straight angles, then they are congruent. If two angles are vertical angles, then they are congruent. If two angles are complementary to the same angle, then they are congruent. (Shared angle between comp statements) If two angles are complementary to congruent angles then they are congruent. (Congruent angles linking comp statements) If two angles are supplementary to the same angle, then they are congruent. (Shared angle between supp statements) If two angles are supplementary to congruent angles then they are congruent. (Congruent angles linking supp statements) If segments are radii of the same circle, then they are congruent. If two sides of a triangle are congruent, then the angles opposite them are congruent (If sides, then angles). If two angles of a triangle are congruent, then the sides opposite them are congruent (If angles, then sides). Properties Addition Property = Segments or angles get bigger Subtraction Property = Segments or angles get smaller Substitution Property = Replacing a segment or angle using congruency Reflexive Property = A segment or angle is congruent to itself Triangle Congruency Theorems Miscellaneous Addition = Adding two angle measures of segment lengths. Subtraction = Subtracting two angle measures or segment lengths. SAS (Side, Included Angle, Side) SSS (Side, Side, Side) ASA (Angle, Included Side, Angle) AAS (Angle, Angle, Non-included Side) HL Postulate (Hypotenuse, Leg, Right Triangle) CPCTC Corresponding Parts of Congruent Triangles are Congruent