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Go To The Head of the Class-Review Game Rules: A question starts with a player. If that player answers correctly he/she keeps his/her seat. If the player misses, then the question goes to the next player. If missed, it goes to the next player... …and continues until someone gets it correct. That student moves to the seat where the question started... …and everyone who missed the question moves back one seat. The object of the game is to occupy and keep the #1 seat. Questions with a limited number of possible responses will not be offered indefinitely. A substitute question will be posed. It is important to listen to previous responses. They will not be repeated for you. The first person to receive a question will have a maximum of 30 seconds to answer. Every person after that has only 10 seconds to reply. Be ready when called upon. If the question is on a yellow screen, expect to solve a problem. Have calculator, paper & pencil ready. If the background is orange, name the definition, property, theorem, etc, that supports the given conclusion. If the question is on a green screen, it requires just a short answer. Time to Play: READY? (begin) 1 2 Then m 1 m 2 180 The Supplement Theorem (The angles in a linear pair are supplementary.) 1 2 Then 1 2 The Vertical Angles Theorem: Vertical Angles are congruent. If A and B are right angles, then A B The Right Angle Theorem: All Right angles are congruent. Two angles are complementary. One is 32 degrees. What is the measure of the other one? ANSWER: 58 degrees What do we call 2 non-adjacent angles that are formed when 2 lines intersect? Answer: Vertical Angles Two angles are supplementary. One angle is 73 degrees, find the measure of the other one. Answer: 107 degrees What do we call 2 lines that intersect to form right angles? Answer: Perpendicular Lines Complete this theorem: If 2 angles are complementary to the same angle…... Answer: … then they are congruent to each other. Remember the “Key” to setting up equations in Geometry... You usually do one of 2 things… - Set two expressions equal to each other Or…. -Add expressions together and set their sum equal to something else. 8x+25 Find x 4x -1 Answer: 8x+25 + 4x - 1 = 180 12x+24=180 12x=156 x=13 7x-10 Find x 5x+12 Answer: 7x-10 = 5x + 12 2x-10 = 12 2x = 22 x = 11 According to the Supplement Theorem, what kind of angles are supplementary? Answer: The angles in a Linear Pair Complete this Theorem: If 2 lines intersect to form congruent adjacent angles, then…. …then the lines are perpendicular. Angle A is 30 degrees. Angle B is complementary to Angle A. Angle C is complementary to Angle B. Find the measure of Angle C. Answer: Angle C is 30 degrees. Angle A is 40 degrees. Angle B is complementary to Angle A. Angle C is supplementary to Angle B. Find the measure of Angle C. Answer: Angle C is 130 degrees. A= 40 => B= 50 If A and B are supplementary, then m A m B 180 The Definition of Supplementary Angles If m A 90 then A is a right angle. The Definition of Right Angle If 1 1 is a right angle, then the lines are perpendicular. The Definition of Perpendicular lines. If A and B are complementary, and A and C are complementary, then B C Congruent Complements Theorem: If 2 angles are complementary to the same angle, they are congruent to each other. If A and B are complementary, then m A m B 90 The Definition of Complementary Angles The Supplement Theorem: The angles in a Linear Pair _____ ____ are supplementary. x y Vertical _______ angles are congruent. COMPLETE: When 2 parallel lines are cut by a transversal... • • • • Corresponding Angles are congruent Alternate Interior Angles are congruent Alternate Exterior Angles are congruent Consecutive Interior Angles are supplementary COMPLETE: When 2 lines are cut by a transversal so that... • • • • Corresponding Angles are congruent Alternate Interior Angles are congruent Alternate Exterior Angles are congruent Consecutive Interior Angles are supplementary …Then the lines are parallel. + = 180 According to their definition, Perpendicular lines ____________ intersect to form right angles. What term describes the two lines? Parallel What term describes the two lines? Skew Identify the type of angles pictured Corresponding Angles Alternate Exterior Angles Consecutive Interior Angles Alternate Interior Angles Vertical Angles Corresponding Angles A Linear Pair p r s 1 2 3 4 5 6 7 8 If p r , and p s then r // s. The Perpendicular Transversal Converse Theorem 1 2 3 4 r s 5 6 7 8 If 3 6 then r // s Alternate Interior Angles Converse Theorem p r s 1 2 3 4 5 6 7 8 If r // s then m 4 m 6 180 Consecutive Interior Angles Theorem p 1 2 3 4 r s 5 6 7 8 If r // s then m 4 m 8 Corresponding Angles Postulate p r s 1 2 3 4 5 6 7 8 m 7 m 8 180 The Supplement Theorem 1 2 3 4 r s 5 6 7 8 If 2 7 then r // s Alternate Exterior Angles Converse Theorem p 1 2 3 4 r s 5 6 7 8 5 8 Vertical Angles Theorem p r s 1 2 3 4 5 6 7 8 If m 3 5 180 then r // s Consecutive Interior Angles Converse Theorem p r s 1 2 3 4 5 6 7 8 If r // s then 1 8 Alternate Exterior Angles Theorem p 1 2 3 4 r 5 6 7 8 s If 3 7 then r // s Corresponding Angles Converse Post. p r s 1 2 3 4 5 6 7 8 If r // s and p r , then p s The Perpendicular Transversal Theorem Some Miscellaneous questions… Which 2 lines are parallel? A. y 23 x 1 B. y 32 x 1 C. y 23 x 1 D. y x 2 3 2 E. y 23 x 1 Which 2 lines are perpendicular? A. y 3x 1 B. y 32 x 1 C. y 23 x 1 D. y 32 x 2 E. y 32 x 1 What kind of line has a slope of zero? Horizontal Find the slope of the line containing the points (3,4) and (0,0): 4 3 Find the slope of the line containing the points (0,4) and (0,0): Undefined Find the slope of the line containing the points (-2,5) and (0,0): 5 2 p r s 75o x o =75 p 55o r s x o =55 65o 115o= x p r s 45o x =135o 110o r s t 60o 70o Which lines are parallel? p 110o r s t 60o 70o Which lines are parallel? p 70o Remember the “Key” to setting up equations in Geometry... You usually do one of 2 things… - Set two expressions equal to each other Or…. -Add expressions together and set their sum equal to something else. Find x o 6x o 3x 6x+3x=180 o 6x x=20 o 3x FIND X (3x+10) o Xo 3x+10+x=90 4x=80 x=20 (3x+10) o =70 X o =20 7x+4 9x-12 Find x 60= 7x+4 9x-12 Find x = 60 7x+4=9x-12 16=2x 8=x 10x+2 9x-12 Find x 9. 10x+2 =102 9x-12 Find x =78 10x-2+9x-12=180 19x-10=180 19x=190 x=10 What kind of triangle has sides of… 4 in. , 6 in. and 3 in.? SCALENE What kind of triangle has Angles of… o o o 90 , 70 , 20 .? RIGHT What kind of triangle has sides of… 5 in. , 5 in. and 3 in.? ISOSCELES What kind of triangle has Angles of… o o o 50 , 60 , 70 .? ACUTE What kind of triangle has Angles of… o o o 60 , 60 , 60 .? EQUIANGULAR What kind of triangle has Angles of… o o o 150 , 10 , 20 .? OBTUSE What kind of triangle has sides of… 5 in. , 5 in. and 5 in.? EQUILATERAL What kind of triangle has Angles of… o o o 150 , 160 , 170 .? NO SUCH TRIANGLE What do we call the congruent sides of an Isosceles Triangle? The LEGS If D ABC has a right angle at B, which side is the Hypotenuse? A. AB B. BC C. AC Which triangle is Impossible? • EQUIANGULAR OBTUSE • SCALENE ISOSCELES • RIGHT EQUILATERAL ALL THREE!! Fill in the blank: 180 m 1 m 2 m 3 _____ 2 1 3 Fill in the blank: m 6 m 1 m 2 _____ 5 2 4 1 3 6 Fill in the blank: m 4 m 3 m 2 _____ 5 2 4 1 3 6 Fill in the blank: m 5 m 3 m 1 _____ 5 2 4 1 3 6 When referring to angle 5, what do we call 3 and 1 ? 5 REMOTE INTERIOR ANGLES 2 4 1 3 6 Fill in the blank: 360 m 4 m 5 m 6 _____ 5 2 4 1 3 6 If this triangle is Equiangular: 60 m 1 _____ 2 1 If this triangle is Equiangular: 2 m 2 120 _____ 1 12x-2 7x+3 9x+11 Set up the equation needed to solve the for x: 7 x 3 12 x 2 9 x 11 180 x6 6x+8 12x-19 4x-7 Set up the equation needed to solve for x: 6 x 8 4 x 7 12 x 19 x 10 7. 50 30 6. 40 100 2. 80 1. 3. 100 60 5. 4.30 80 50 8. 50 8. 1306. 50 5. 9. 70 7. 60 60 4. 50 1. 110 2. 70 50 603. Given the two triangles are congruent, complete the following: M TKM ABC _______ A C T B K Which postulate, if any, could be used to prove the triangles are congruent? I L K SAS J M Which postulate, if any, could be used to prove the triangles are P congruent? Q N SSS R Which postulate, if any, could be used to prove the triangles are congruent? O T NONE S V U Which postulate, if any, could be used to prove the triangles are congruent? A D ASA B C What additional information is needed to prove ABC ZVR by SSS if you already Know: BC VR AB ZV AC ZR What additional information is needed to prove ABC ZVR by SAS if you already Know: BC VR C R AC ZR What additional information is needed to prove ABC ZVR by ASA if you already Know: BC VR C R B V THE END