1. 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)

2. 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 2-1 2-2 2-3 5-4 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

3. 1-8 8-1 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 ∠8 3-1 3-2 3-3 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

4. 1 st Semester Geometry Notes page 4 180 – 3-5 Polygon Angle Sum Thms n = number of sides Interior angle Exterior angle for regular polygons 3-6 3-7 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)

5. 1 st Semester Geometry Notes page 5 7-1 Ratios and Proportions 7-2 Similarity 7-3 Proving Triangles Similarity SSS, SAS, AA =

6. 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 6 7-4 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.

7. 1 st Semester Geometry Notes page 7 4-2 4-3 4-6 Proving Triangles Congruent SSS SAS ASA AAS HL CPCTC is an abbreviation of the phrase “Corresponding Parts of Congruent Triangles are Congruent.” 4-4 4-7 Using CPCTC in Proofs

8. 1 st Semester Geometry Notes page 8 5-5 Triangle Inequalities 5-1 5-2 5-3 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