Geometry Final Exam Review Guide A. Linear Equations 1. Parallel lines have slopes that are ___________________. 2. Perpendicular lines have slopes that are _______________________. Write an equation of a line that is perpendicular to 2x + 3y = 9 and passes through (6,1) 3. Write an equation of a line that is perpendicular to, and bisects, the segment joining (1,4) and (9,4) B. Quadratic and Linear Systems Find the solution to: C. Tools of Geometry 1. Write the Midpoint formula: 2. Write the Distance formula: 3. Write the slope formula: 4. Draw the following “Locus” models: a. A given distance from a point: b. A given distance from a line: c. Equidistant from parallel lines: d. Equidistant from two points: e. Equidistant from intersecting lines or a given angle: D. Parallel Lines and Transversals Name the congruent angles and their relationship: (a is parallel to b) 1 2 a 3 5 4 6 b 7 8 E. Triangles 1. An exterior angle of a triangle is equal to _______________________________________________________ Draw a diagram that justifies this statement: 2. The sum of any two sides of a triangle must be ________________ _______________________________________________________ 3. Name three lengths that can be sides of a triangle: Name three lengths that cannot be sides of a triangle: 4. The longest side of a triangle is opposite the ______________________ The shortest side of a triangle is opposite the ______________________ F. Polygons 1. The sum of the exterior angles of any polygon is ______________. 2. The sum of the interior angles of a polygon is ________________ 3. To prove a quadrilateral is a parallelogram show: 4. To prove a quadrilateral is a rhombus show: 5. To prove a quadrilateral is a square show: 6. To prove a quadrilateral is a trapezoid show: G. Circles 1. Equation of a circle whose center is (0,0) 2. Equation of a circle whose center is (h,k) 3. Draw a central angle and the measure of its angle and the arc it cuts off: 4. Draw an inscribed angle and the measure of its angle and the arc it cuts off: 5. Draw intersecting chords, and show the relationship of one angle and the arcs the segments cut off. 6. Draw intersecting chords and show the relationship between each of the pieces of the chords. 7. Draw a circle with 2 tangents drawn from the same external point. Connect the two points of tangency with a chord. What is the relationship between the lengths of the tangents? H. Right Triangle Similarity: Identify parts of diagrams and write the two proportions: I. Transformations Reflection in x axis: Reflection in y axis: Reflection in y=x : Reflection in origin: Reflection in y=-x : Translate according to the rule (x +a, y + b) or Ta,b Rotate 90◦ : Rotate 180◦ Dilate by “k” (x,y) would be: Composition of functions: Transform the point (3,-2) according to the rule T-3,4 ◦ rx-axis ***Which transformation goes first? Vocabulary: Invariant Isometry Opposite Isometry/direct isometry J. Logic 1. When is an “and” statement true? 2. When is an “or” statement true? 3. When is a conditional statement false? 4. When is a biconditional statement true? 5. Related conditionals: If I study a lot, then I will do well. Converse: Inverse: Contrapositive: Which of these statements is always true when the conditional is true? In other words, which statement is always logically equivalent to the original conditional?