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Relationships in Triangles

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This is a review game for a teacher to use in a geometry class. It goes over relationships in triangles, including bisetors, medians, altitudes, and inequalities and triangles.

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Relationships in Triangles

  1. 1. Bisectors, Indirect Proof Indirect Proof The Triangle InequalitiesMedians, & Inequality Involving TwoAltitudes Triangles 2 points 2 points 2 points 2 points 2 points 3 points 3 points 3 points 3 points 3 points 4 points 4 points 4 points 4 points 4 points 5 points 5 points 5 points 5 points 5 points 6 points 6 points 6 points 6 points 6 points 7 points 7 points 7 points 7 points 7 points 8 points 8 points 8 points 8 points 8 points 9 points 9 points 9 points 9 points 9 points Team 1 : Team 2 :
  2. 2. Bisectors, Medians, & Altitudes: 2 PointsIn ∆GHJ, HP=5x-16, H NPJ=3x+8, m<GJN=6y-3,m<NJH=4y+23, &m<HMG=4z+14 G P Stop! M Time’s Up!The Question Is : JGP is a median of ∆GHJ. Find HJ.The Answer Is :88
  3. 3. Bisectors, Medians, & Altitudes: 3 PointsIn ∆GHJ, HP=5x-16, H NPJ=3x+8, m<GJN=6y-3,m<NJH=4y+23, &m<HMG=4z+14 G P Stop!The Question Is : M Time’s bisector.Find m<GJN if JN is an angle Up! JThe Answer Is :150
  4. 4. Bisectors, Medians, & Altitudes: 4 PointsIn ∆GHJ, HP=5x-16, H NPJ=3x+8, m<GJN=6y-3,m<NJH=4y+23, &m<HMG=4z+14 G P Stop! MThe Question Is : Time’s find the value ofIf HM is an altitude of ∆GHJ, Up! Jz.The Answer Is :19
  5. 5. Bisectors, Medians, & Altitudes: 5 PointsThe Question Is :All of the angle bisectors of a triangle meet atthe _________. Stop! Time’s Up!The Answer Is :incenter
  6. 6. Bisectors, Medians, & Altitudes: 6 PointsCP is an altitude, CQ is the Cangle bisector of <ACB, and R isthe midpoint of AB.The Question Is : Stop!and m<QCB=42+x. Time’s Up! PFind m<ACQ if m<ACB=123-x A Q R BThe Answer Is :m<ACQ = 55
  7. 7. Bisectors, Medians, & Altitudes: 7 PointsCP is an altitude, CQ is the Cangle bisector of <ACB, and R isthe midpoint of AB.The Question Is : Stop!Find AB if AR=3x+6 andRB=5x-14 Time’s Up! P A Q R BThe Answer Is :AB = 72
  8. 8. Bisectors, Medians, & Altitudes: 8 PointsThe Question Is :In ∆RST, if the point P is the midpoint of RS, Stop!then PT is a(n) ________.The AnswerTime’s Up! Is :median
  9. 9. Bisectors, Medians, & Altitudes: 9 PointsThe Question Is :What are the special segments of triangles? Stop! Time’s Up!The Answer Is :Perpendicular bisectors, medians, anglebisectors, and altitudes
  10. 10. Indirect Proof: 2 PointsThe Question Is :When using _________, you assume that theconclusion false and then show that this assumption Stop!leads to a contradiction of the hypothesis, or someother accepted fact, such a definition, postulate, Time’s Up!theorem, or corollary.The Answer Is :Indirect reasoning
  11. 11. Indirect Proof: 3 PointsThe Question Is :True or False: Another name for an indirectproof is a proof by contradiction. Stop! Time’s Up!The Answer Is :True
  12. 12. Indirect Proof: 4 PointsThe Question Is :What are the three steps of writing an indirect proof.The Answer Is :1. Assume that the conclusion is false Stop!2. Show that this assumption leads to a Time’s Up! contradiction of the hypothesis, or some other fact, such as a definition, postulate, theorem, or corollary3. Point out that because the false conclusion leads to an incorrect statement, the original conclusion must be true
  13. 13. Indirect Proof: 5 PointsThe Question Is :State the assumption you would make tostart an indirect proof of the following Stop!statement: EF is not a perpendicular bisector. Time’s Up!The Answer Is :EF is a perpendicular bisector.
  14. 14. Indirect Proof: 6 PointsThe Question Is :State the assumption you would make tostart an indirect proof of the following Stop!statement: If 5x < 25, then x < 5. Time’s Up!The Answer Is :x>5
  15. 15. Indirect Proof: 7 PointsThe Question Is :State the assumption you would make to start anindirect proof of the following statement: If arational number is any number that can be Stop!expressed as a/b, where a and b are integers and bis not equal to 0, 6 is a rational number. Time’s Up!The Answer Is :6 cannot be expressed as a/b, wherea & b are integers and b is not equalto 0.
  16. 16. Indirect Proof: 7 PointsThe Question Is :State the assumption you would make to start anindirect proof of the following statement: The anglebisector of the vertex angle of an isosceles triangle Stop!is also an altitude of the triangle. Time’s Up!The Answer Is :The angle bisector of the vertex angle of an isoscelestriangle is not an altitude of the triangle.
  17. 17. Indirect Proof: 9 PointsThe Question Is :State the assumption you would make to start anindirect proof of the following statement: Two lines Stop!that are cut by a transversal so that alternateinterior angles are congruent are parallel.The Answer Is : Time’s Up!The lines are not parallel
  18. 18. Inequalities & Triangles: 2 PointsThe Question Is :What is the definition of an inequality?The Answer Is : Stop!For any real numbers a and b,Up!if and only if Time’s a > bthere is a positive number c such that a = b + c.
  19. 19. Inequalities & Triangles: 3 PointsThe Question Is :What are the four properties of Inequalities forReal Numbers? Stop!The Answer Is : Time’s Up!Comparison Property, Transitive Property,Addition and Subtraction Properties, &Multiplication and Division Properties
  20. 20. Inequalities & Triangles: 4 PointsThe Question Is :What does the “Comparison Property” say? Stop!The Answer Is : Time’s Up!a < b, a = b, or a > b
  21. 21. Inequalities & Triangles: 5 PointsThe Question Is : 7 4Use the Exterior AngleInequality Theorem to list Stop!all angles that satisfy thestated condition: measuresless than m<1 Time’s Up! 5 6 8 3 2 1The Answer Is :<4, <5, <6
  22. 22. Inequalities & Triangles: 6 PointsThe Question Is : 7 4Determine the angle with theGreatest measure: <1, <2, <3. Stop!The Answer Is : Time’s Up! 5 8 2 1 6 3<1
  23. 23. Inequalities & Triangles: 7 PointsThe Question Is :Determine the angle with the 8Greatest measure: <8, <5, <7. 7 Stop! 5The Answer Is : Time’s Up!<5
  24. 24. Inequalities & Triangles: 8 PointsThe Question Is : 6Determine the angle with the 8Greatest measure: <6, <7, <8. 7 Stop!The Answer Is :Time’s Up!<8
  25. 25. Inequalities & Triangles: 9 PointsThe Question Is :Determine the angle with the 6Greatest measure: <1, <6, <9. 1 Stop! 9The Answer Is : Time’s Up!<1
  26. 26. The Triangle Inequality : 2 PointsThe Question Is :What is the “Triangle Inequality Theorem?”The Answer Is : Stop!The sum of the lengths of anyUp! Time’s two sides of a triangle isgreater than the length of the third side.
  27. 27. The Triangle Inequality : 3 PointsThe Question Is :What is the “Triangle Inequality Theorem” used todetermine? Stop!The Answer Is : Time’s Up!Whether three segments can form a triangle.
  28. 28. The Triangle Inequality : 4 PointsThe Question Is :If a line is horizontal, the shortest distance from a pointto that line will be along a _______ line. Likewise, the Stop!shortest distance from a point to a vertical line liesalong a ________ line. Time’s Up!The Answer Is :vertical, horizontal
  29. 29. The Triangle Inequality : 5 PointsThe Question Is :The ________ segment from a point to a line is theshortest segment from the point to the line. Stop! Time’s Up!The Answer Is :perpendicular
  30. 30. The Triangle Inequality : 6 PointsThe Question Is :Can the following lengths be the lengths of the sides ofa triangle: 1, 2, 3? Explain. Stop!The Answer Is : Time’s Up!No; 1 + 2 is not greater than 3
  31. 31. The Triangle Inequality : 7 PointsThe Question Is :Find the range for the measure of the third side: 5 and11. Stop!The Answer Is :Time’s Up!6 < n <16
  32. 32. The Triangle Inequality : 8 PointsThe Question Is :Determine whether or not the given measures can be Stop!the lengths of the sides of a triangle: 9, 21, 20. Explain. Time’s Up!The Answer Is :Yes; 9 + 20 > 21
  33. 33. The Triangle Inequality : 9 PointsThe Question Is :Find the range for the measure of the third side of thetriangle: 21 and 47. Stop!The Answer Is :Time’s Up!26 < n < 68
  34. 34. Inequalities Involving 2 Triangles: 2 PointsThe Question Is :What does the “SAS Inequality” state?The Answer Is : Stop!Two sides of a triangle are congruent to two sides ofanother triangle. Time’s Up! in the first If the included angletriangle has a greater measure than the included anglein the second triangle, then the 3rd sideOf the first triangle is longer than the3rd side of the second.
  35. 35. Inequalities Involving 2 Triangles: 3 PointsThe Question Is :What is another name for the “SAS InequalityTheorem?” Stop!The Answer Is : Time’s Up!The “Hinge Theorem.”
  36. 36. Inequalities Involving 2 Triangles: 4 PointsThe Question Is :What does the “SSS Inequality Theorem” state?The Answer Is : Stop! to 2 sides ofIf 2 sides of a triangle are congruent Time’s other, then the angle rd Up!another triangle, and the 3 side in one triangle is rdlonger than the 3 side in thebetween the pair of congruent sides in the 1st triangleis greater than the corresponding angle in the 2ndtriangle.
  37. 37. Inequalities Involving 2 Triangles: 5 Points 15 AThe Question Is : D 20Write an inequalityrelating AB and CD. 50 B Stop!The Answer Is : 15AB < CD Time’s Up! C
  38. 38. Inequalities Involving 2 Triangles: 6 PointsThe Question Is : x+5Write an inequality 45relating AB and CD. 3x - 7 Stop!The Answer Is : Time’s Up!7/3 < x <6
  39. 39. Inequalities Involving 2 Triangles: 7 PointsThe Question Is : 4 C BWrite an inequality relating 6the given pair of angles Stop!or segments: AB, FD. 9 6 9 DThe Answer Is : Time’s Up! A F 6 10AB > FD
  40. 40. Inequalities Involving 2 Triangles: 8 PointsThe Question Is : 4 C BWrite an inequality relating 6the given pair of angles 9or segments: m<BDC,m<FDB. Stop! 9 6 D Time’s Up! A 10 F 6The Answer Is :M<BDC < m<FDB
  41. 41. Inequalities Involving 2 Triangles: 9 PointsThe Question Is : 4 C BWrite an inequality relating 6the given pair of anglesm<DBF. Stop!or segments: m<FBA, 9 6 9 DThe Answer Is : Time’s Up! A 10 F 6m<FBA > m<DBF

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