Report

Jeopardy Basic Distance Geometry and Parallel and Definitions Midpoint Perpendicular Angles Proofs 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500 Category 1 100 The three undefined terms of geometry. Category 1 100 Point, Line, Plane 200 Category 1 What is the definition of a ray, and name the ray below. R B T Category 1 200 Ray: Straight arrangement of points that begins at an endpoint and extends forever in one direction. BR or BT Category 1 300 Name the following figure and give the definition. L P W Category 1 300 Angle: Two rays that share a common endpoint, but are not the same line. ∠P or ∠ LPW or ∠ WPL Category 1 400 A point that lies exactly halfway between two points, dividing a line segment into two congruent line segments. Category 1 400 A Midpoint Category 1 500 A rigid motion that “slides” each point of a figure the same distance and direction. Category 1 500 Translation Category 2 100 What is the midpoint formula? Category 2 100 x1 x 2 y 1 y 2 , 2 2 Category 2 200 Find the midpoint of the line segment AB, if A(3, - 6) and B(-9, - 4). Category 2 200 Midpoint AB = (-3, -5) 300 Category 2 What is this formula used for: d x2 x1 y 2 y 1 2 2 Category 2 300 Distance Formula Category 2 400 What is the distance between the points A and B, if A(4, 2) and B (-7, 6) Category 2 d = √137 400 Category 2 500 Find the midpoint and the distance between the points M(-3, 12) and N(4, 8). Category 2 500 Midpoint of MN = (½, 10) Distance of MN = √65 Category 3 100 Fill in the blanks: Parallel lines have the same _______. Perpendicular lines have slopes that are opposite _________. Category 3 100 Fill in the blanks: Parallel lines have the same Slope. Perpendicular lines have slopes that are opposite Recipricals. Category 3 200 Find the slope of a line parallel to the given line: Line n : 2y + 3x = 4 Category 3 200 Slope = -3/2 Category 3 300 Find the slope of a line perpendicular to the given line: Line k: 8x – 4y = 6 Category 3 300 Slope = -½ Category 3 400 Determine if the lines would be parallel, perpendicular, coinciding or intersecting. 2y - 6x = 5 9y = -3x - 18 Category 3 400 Perpendicular: y = 3x + 5/2 y = -1/3x - 2 Category 3 500 Write the equation of a line parallel to line m and passing through the point (8, -6). line m: y = ¾x + 7 Category 3 500 Slope = ¾ y = ¾x - 12 100 Category 4 Name all the pairs of corresponding angles in the figure: 1 2 4 3 5 6 7 8 100 Category 4 <1 and <5, <2 and <6, <4 and <8, <3 and <7 1 2 4 3 5 6 7 8 Category 4 200 The complement of an angle is 4 times greater then the angle. Find the measure of the angle and it’s complement. 200 Category 4 The angle = o 18 The complement of the o angle = 72 300 Category 4 If the measure of angle 1 is 43o, what is the measure of angle 8 and angle 3? 1 2 4 3 5 6 7 8 300 Category 4 m∠1 = 43o m∠3 = 43o m∠8 = 137o 1 2 4 3 5 6 7 8 400 Category 4 Find the measure of each angle: 5x - 12 3x + 8 400 Category 4 x = 23o 3(x) + 8 = o 77 5(x) – 12 = 103o Category 4 500 The supplement of an angle is two thirds the measure of the angle. Find the measure of the angle and its supplement. 500 Category 4 The angle = o 108 The supplement of the o angle is 72 Category 5 100 Identify the hypothesis and the conclusion of the following statement: If a parallelogram is a square, then it is a rhombus. Category 5 100 Hypothesis: a parallelogram is a square Conclusion: it is a rhombus Category 5 200 Write the inverse of the following statement and determine if it is true. If two angles are vertical angles, then the angles are congruent. Category 5 200 If two angles are congruent, then they are vertical angles. False, angles can be congruent without being vertical angles. Congruent means that the angles have the same measure. Category 5 300 Write a two column proof: Given: ∠1 and ∠2 are supplementary. Prove: ∠1 + ∠2 = 180o 300 Category 5 Given: ∠1 and ∠2 are supplementary. Prove: ∠1 + ∠2 = 180o Statement 1. ∠1 and ∠2 are supplementary 2. ∠1 + ∠2 = 180o Reason 1.Given 2. Definition of supplementary angles Category 5 Fill in the missing parts of the proof. Given:∠ABC and ∠CBD are a linear pair Prove: ∠ABC + ∠CBD = 180o Statement 1. ∠ABC and ∠CBD are a linear pair 2. ∠ABC and ∠CBD are supplementary 3. ∠ABC + ∠CBD = 180o C A B D Reason 1. 2. 3. 400 400 Category 5 Statement 1. ∠ABC and ∠CBD are a linear pair 2. ∠ABC and ∠CBD are supplementary 3. ∠ABC + ∠CBD = 180o Reason 1. Given 2. Linear Pair Postulate 3. Definition of Supplementary Angles C A B D Category 5 Fill in the missing parts of the proof. Given: line n // line m and line t is a t transversal 1 23 Prove: ∠4 ≌ ∠6 4 Statement 1. 2. ∠4 ≌ ∠8 3. ∠8 ≌ ∠6 4. Reason 1. Given 2. Corresponding Angles Postulate 3. 4. Transitive Property of Congruence 500 n 5 67 8 m Category 5 Statement 1. line n // line m 2. ∠4 ≌ ∠8 3. ∠8 ≌ ∠6 4. ∠4 ≌ ∠6 t 1 23 4 500 n m 5 67 8 Reason 1. Given 2. Corresponding Angles Postulate 3. Vertical Angle Theorem 4. Transitive Property of Congruence