1-3 Points, Lines, Planes plane M or plane ABC (name with 3 pts) A point A Points A, B are collinear Points A, B, and C are coplanar Intersection of two distinct lines is a point Intersection of two distinct planes is a line 1-4 Segments, Rays, Parallel Lines, Planes Segment AB or Opposite rays share same endpoint Opposite rays are collinear Parallel Lines -Never intersect -Extend in the same directions -Coplanar Skew Lines -Never intersect -Extend in different directions -Noncoplanar Parallel Planes -Can never intersect 1-5 Measuring Segments AB is the abbreviation for the distance between points A and B. Segment Addition Postulate Midpoint B is exactly halfway between A and C B is the average coordinate of A and C 1-6 Measuring Angles 1 st Semester Geometry Notes page 1 vertex Congruent Angles m  1 = m  2 (the measure of angle 1 equals the measure of angle 2)  1 ≅  2 (Angle 1 is congruent to angle 2) (May also be indicated by arc on both angles)

Angle Addition Postulate m  AOB + m  BOC = m  AOC Pairs of Angles  1 and  2 are adjacent angles -No interior points in common -Share the same vertex R -Share common side  1 and  3  2 and  4 Vertical Angles -Non-adjacent; -Formed by two intersecting lines -Are congruent C ompl. C orner Suppl. Straight Linear Pairs -Form a straight angle -Are supplementary (sum = 180) 1-1 Inductive Reasoning Conditional: If a, then b statement a is the hypothesis; b is the conclusion Converse: Switch the hypothesis and conclusion. If b, then a. Truth value of a statement: Either True or False, where True means always true Biconditional: Both the conditional and its converse are true. You can combine both statements with if and only if. a if and only if b. Addition Property If a = b, then a + c = b + c Subtraction Property If a = b, then a – c = b – c Multiplication Property If a = b, then a * c = b * c Division Property If a = b and c ≠ 0, then a/c = b/c Reflexive Property a = a Symmetric Property If a = b, then b = a Transitive Property If a = b and b = c, then a = c Substitution Property If a = b, then b can replace a in any expression Distributive Property a(b + c) = ab + ac Deductive Reasoning Law of Detachment: If a, then b. (True) Given: a is True b is therefore True. Law of Syllogism If a, then b. (True) If b, then c. (True) If a, then c must be True. A B A B C If A is falls to the right, then B falls to the right Given: A falls to the right is True Then: B falls to the right. If B is falls to the right, then C falls to the right. If A falls to the right, then C falls to the right. 2-4 Algebraic Properties 1 st Semester Geometry Notes page 2

Pythagorean Theorem, Midpoint, Distance Formula (leg1) 2 + (leg2) 2 = hypotenuse 2 True only for right triangles Pythagorean Theorem 1 st Semester Geometry Notes page 3 Classifying Triangles Let a, b, c be the lengths of the sides of a triangle, where c is the longest Acute: c 2 < a 2 + b 2 Right: c 2 = a 2 + b 2 Obtuse: c 2 > a 2 + b 2 Distance between 2 points -Use the Pythag. Thm Midpoint (average x, average y) Transversal: line that cuts across two or more lines Congruent if and only if l and m are parallel Supplementary if and only if l and m are parallel Same-side exterior: ∠1 and ∠4 ∠5 and ∠ Parallel Lines and Angles Vertical angles are congruent Linear pairs are supplementary 3-4 Triangle Sum Thm, Exterior Angle Thm A triangle is isosceles if and only if the base angles are congruent. A triangle is equilateral if and only if the triangle is equiangular 4-5 Isosceles and Equilateral Triangles

1 st Semester Geometry Notes page – 3-5 Polygon Angle Sum Thms n = number of sides Interior angle Exterior angle for regular polygons Graphing Equations of Lines Any point on the line must satisfy the equation of the line (y = mx + b) Parallel lines have equal slopes (same steepness) Perpendicular lines have slopes that are negative reciprocals of each other Standard Form: Ax + By = C Point-Slope Form: y – y1 = m (x – x1) 9-1 Translations: (x, y) → (x+a, y+b) 9-2 Reflections: Preimage and image are -on opposite sides of line of reflect. -equidistant from line of reflection Reflect about x-axis (x, y) → (x, -y) Reflect about y-axis (x, y) → (-x, y) Reflect about y = x (x, y) → (y, x) 9-3 Rotations about origin: For each 90° of rotation, switch the x and y coordinates; then determine signs based on the quadrant after rotation 9-4 Symmetry Preimage: before the transformation Image: after the transformation Isometry: size and shape stay the same Reflections, Translations, and Rotations are isometries 9-5 Dilations Enlargement: Multiply both x and y by a scale factor k greater than 1 (x, y) → (kx, ky) Reduction: Multiply both x and y by a scale factor k between 0 and 1 (x, y) → (kx, ky) Vertical stretch Multiply the y only by a scale factor k greater than 1 (x, y) → (x, ky) Horizontal shrinkage Multiply the x only by a scale factor k between 0 and 1 (x, y) → (kx, y)

1 st Semester Geometry Notes page Ratios and Proportions 7-2 Similarity 7-3 Proving Triangles Similarity SSS, SAS, AA =

Small legMedium legHypotenuse ∆1abc ∆2rha ∆3hsb 1)Redraw and label triangles. 2)Fill in the table with given information 3)Use proportions or Pythag. Thm to solve for missing lengths 1 st Semester Geometry Notes page Similarity in Right Triangles 7-5 Proportions in Triangles in a triangle 4-1 Congruent Polygons Two polygons are congruent if they have the same size and shape. Two polygons are congruent if and only if all corresponding sides and corresponding angles are congruent.

1 st Semester Geometry Notes page Proving Triangles Congruent SSS SAS ASA AAS HL CPCTC is an abbreviation of the phrase “Corresponding Parts of Congruent Triangles are Congruent.” Using CPCTC in Proofs

1 st Semester Geometry Notes page Triangle Inequalities Special Segments in Triangles Altitudes (vertex to opposite side at right angles – Orthocenter Perpendicular Bisectors (90 degrees through midpoint of a side) – Circumcenter Medians (vertex to midpoint of opposite side) – Centroid Angle Bisectors (vertex to opposite side through line splitting the vertex angle in half– Incenter Given two sides a and b, the third side the triangle with length c must satisfy | a – b | < c < a + b