Reflexive Property of Congruence: figure A figure A Symmetric Property of Congruence: If figure A figure B, then figure B figure A. If , then . Transitive Property of Congruence If figure A figure B and figure B figure C, then figure A figure C. If and , then . Chapter 2 Properties, Postulates and Theorems Geometric Reasoning Theorem Name What it says… Key Words Picture Linear Pair Theorem 2-6-1 If two angles form a linear pair, then they are supplementary. Two angles Linear pair Supplementary Congruent Supplements Theorem 2-6-2 If two angles are supplementary to the same angle (or to two congruent angles), then the two angles are congruent. Two angles Supplementary Congruent Right Angle Congruence Theorem 2-6-3 All right angles are congruent. Right angle Congruent
Perpendicular Transversal Theorem In a plane, if a transversal is perpendicular to one of 2 parallel lines, then it is perpendicular to the other. Perpendicular Transversal parallel 3-4-3 If 2 coplanar lines are perpendicular to the same line, then the 2 lines are parallel to each other. Perpendicular Parallel Chapter 4 Properties, Postulates and Theorems Congruent Triangles Postulate or Theorem Name What it says Sketch 4-2 Triangle Sum Theorem (4-2-1) The sum of the angle measures of a triangle is 180°. Exterior Angle Theorem The measure of an exterior angle is equal to the sum of its 2 remote interior angles. Third Angles Theorem (4-2-5) If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. Ways to prove that 2 triangles are congruent 4-4 Side-Side-Side (SSS) Congruence If three sides of one triangle are congruent to three sides of another triangle, THEN THE TRIANGLES ARE CONGRENT. Side-Angle-Side (SAS) Congruence If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, THEN THE TRIANGLES ARE CONGRENT.
Special Parallelograms All About a Rectangle! Characteristics of ... Proving that it is one ... Definition: An equiangular quadrilateral 6-4-1: All rectangles are parallelograms. 6-4-2: Diagonals are congruent. 6-5-1: A parallelogram with one right angle 6-5-2: A parallelogram with congruent diagonals All About a Rhombus! Characteristics of ... Proving that it is one ... Definition: An equilateral quadrilateral 6-4-3: All rhombuses are parallelograms. 6-4-4: Its diagonals are perpendicular. 6-4-5: Each diagonal bisects a pair of opposite angles. 6-5-3: A parallelogram with one pair of consecutive congruent sides 6-5-4: A parallelogram with perpendicular diagonals 6-5-5: A parallelogram whose diagonal bisects a pair of opposite angles
All About a Square! Characteristics of ... Proving that it is one ... Definition: An equiangular quadrilateral 6-4-1: All rectangles are parallelograms. 6-4-2: Diagonals are congruent. Prove that the quadrilateral is both a rectangle and a rhombus! Other Special Quadrilaterals Kite Trapezoid Isosceles Trapezoid Definition: A quadrilateral with exactly two pairs of consecutive, congruent sides. 6-6-1: Its diagonals are perpendicular. 6-6-2: Non-vertex angles are congruent One diagonal is the perpendicular bisector of the other. One diagonal bisects each vertex angle. Definition: A quadrilateral with exactly one pair of parallel sides. Consecutive angles between the bases are supplementary. The length of the midsegment is the average of the lengths of the two bases. Definition: A trapezoid whose non-parallel sides are congruent. Base angles are congruent. Diagonals are congruent.