Jeopardy Basic Geometry Definitions Distance and Midpoint Parallel and Perpendicular Angles Proofs

Category The three undefined terms of geometry.

Category Point, Line, Plane

Category What is the definition of a ray, and name the ray below. B R T

Category Ray: Straight arrangement of points that begins at an endpoint and extends forever in one direction. BR or BT

Category Name the following figure and give the definition. L P W

Category Angle: Two rays that share a common endpoint, but are not the same line. ∠ P or ∠ LPW or ∠ WPL

Category A point that lies exactly halfway between two points, dividing a line segment into two congruent line segments.

Category A Midpoint

Category A rigid motion that “slides” each point of a figure the same distance and direction.

Category Translation

Category What is the midpoint formula?

Category 2 100

Category Find the midpoint of the line segment AB, if A(3, - 6) and B(-9, - 4).

Category Midpoint AB = (-3, -5)

Category What is this formula used for:

Distance Formula Category 2 300

Category What is the distance between the points A and B, if A(4, 2) and B (-7, 6)

Category d = √137

Category Find the midpoint and the distance between the points M(-3, 12) and N(4, 8).

Category Midpoint of MN = (½, 10) Distance of MN = √65

Category Fill in the blanks: Parallel lines have the same _______. Perpendicular lines have slopes that are opposite _________.

Category Fill in the blanks: Parallel lines have the same Slope. Perpendicular lines have slopes that are opposite Recipricals.

Category Find the slope of a line parallel to the given line: Line n : 2y + 3x = 4

Category 3 Slope = -3/2 200

Category Find the slope of a line perpendicular to the given line: Line k: 8x – 4y = 6

Category Slope = -½

Category Determine if the lines would be parallel, perpendicular, coinciding or intersecting. 2y - 6x = 5 9y = -3x - 18

Category Perpendicular: y = 3x + 5/2 y = -1/3x - 2

Category Write the equation of a line parallel to line m and passing through the point (8, -6). line m: y = ¾x + 7

Category Slope = ¾ y = ¾x - 12

Category Name all the pairs of corresponding angles in the figure:

100 Category 4 <1 and <5, <2 and <6, <4 and <8, <3 and <

200 Category 4 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 = 18 o The complement of the angle = 72 o

300 Category If the measure of angle 1 is 43 o, what is the measure of angle 8 and angle 3?

300 Category m ∠1 = 43 o m ∠3 = 43 o m ∠8 = 137 o

400 Category 4 Find the measure of each angle: 3x + 8 5x - 12

400 Category 4 x = 23 o 3(x) + 8 = 77 o 5(x) – 12 = 103 o

500 Category 4 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 = 108 o The supplement of the angle is 72 o

Category Identify the hypothesis and the conclusion of the following statement: If a parallelogram is a square, then it is a rhombus.

100 Category 5 Hypothesis: a parallelogram is a square Conclusion: it is a rhombus

200 Category 5 Write the inverse of the following statement and determine if it is true. If two angles are vertical angles, then the angles are congruent.

200 Category 5 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.

300 Category 5 Write a two column proof: Given: ∠1 and ∠2 are supplementary. Prove: ∠1 + ∠2 = 180 o

300 Category 5 Given: ∠ 1 and ∠ 2 are supplementary. Prove: ∠ 1 + ∠ 2 = 180 o StatementReason 1. ∠1 and ∠2 are supplementary 1.Given 2. ∠1 + ∠2 = 180 o 2. Definition of supplementary angles

400 Category 5 Fill in the missing parts of the proof. Given: ∠ABC and ∠CBD are a linear pair Prove: ∠ABC + ∠CBD = 180 o StatementReason 1. ∠ABC and ∠CBD are a linear pair ∠ABC and ∠CBD are supplementary ∠ABC + ∠CBD = 180 o 3. AB C D

400 Category 5 StatementReason 1. ∠ABC and ∠CBD are a linear pair 1. Given 2. ∠ABC and ∠CBD are supplementary 2. Linear Pair Postulate 3. ∠ABC + ∠CBD = 180 o 3. Definition of Supplementary Angles AB C D

500 Category 5 Fill in the missing parts of the proof. Given: line n // line m and line t is a transversal Prove: ∠4 ≌ ∠ n m t StatementReason 1.1.Given 2. ∠4 ≌ ∠8 2. Corresponding Angles Postulate 3. ∠8 ≌ ∠ Transitive Property of Congruence

500 Category 5 StatementReason 1. line n // line m1.Given 2. ∠4 ≌ ∠8 2. Corresponding Angles Postulate 3. ∠8 ≌ ∠6 3. Vertical Angle Theorem 4. ∠4 ≌ ∠6 4. Transitive Property of Congruence n m t