Review Sheet Chapter Five

1. Review Sheet Chapter Five • Sides and Angles Related: (Virtual Alligator!!) • Biggest side is opposite the biggest angle • Middle side is opposite the middle angle • Smallest side is opposite the smallest angle • Given two sides, find the range of the third: • Largest side – Smallest side < third side < Largest side + Smallest side • Angles or Sides in order (largest to smallest or smallest to largest): • Put given numbers (side lengths or angle measurements) into order asked for in problem • Replace the numbers with what they represent in letters (2 letters for a side, 1 for an angle) • Put in the missing letter(s) of the triangle (if you have 2 letters, now you have 1 letter) • Now you have the opposite (given sides  order angles or given angles  order sides) in proper order • Given two angles or sides and the middle side or angle: • The middle side or angle must lie between the largest and smallest side or angle: • smallest side < middle side < largest side • smallest angle < middle angle < largest angle • Exterior Angle Inequality Theorem: • Exterior angle > either of the Remote angles • Test Taking Tips: • Use your eyes and scratch paper to help “measure” the angles and sides

2. Select all answers: Given: Triangle ABC with AB = 42 and BC = 20 Which of the following are possible lengths for AC? 12 20 22 32 42 50 62 70 third side must: 42 – 20 < 3rd side < 42 + 20 22 < 3rd side < 62 all answers 32, 42, and 50 fit the inequality

3. Triangles and Logic • SSM: • any two sides bigger than 3rd third side must: 14 – 8 < 3rd side < 14 + 8 6 < 3rd side < 22 all answers except A fit inequality above

4. Triangles and Logic • SSM: • Use ruler or scrap paper to measure AB and estimate BC Angles: A = 60, C = 50 and B must be 70 (3 angles = 180) Since BC is opposite the 60° angle it is the middle length side, and must be between 10 (smallest) and 12 (longest)

5. Triangles and Logic • SSM: • not much help Any two sides of a triangle must be bigger than the third

6. Triangles and Logic • SSM: • three can’t and only one works Take the smallest two numbers add them together if they are greater than the third, then we can have a triangle answers F, G and H all fail the test

7. Triangles and Logic • SSM: • Remember the virtual alligatorlargest stick  largest mouth Order the measures of angles from smallest to largest: 45 < 65 < 70 Replace with the letter of the angles A < B < C Put in the missing letters of the triangle BC < AC < AB Now the sides are ordered from largest to smallest: BC < AC < AB

8. Ch 5 Coordinate Relations and Transformations • SSM: • any two sides bigger than third 19 67 Use the following formula to find the bounds of the third side: Lg – sm < third side < Lg + sm 43 – 24 < third side < 43 +24 19 < third side < 67

9. Ch 5 Coordinate Relations and Transformations • SSM: • draw triangle Draw a triangle and label the sides and angles with what is given Find the missing angle (180 – (45 + 68) = 180 – 113 = 67) Put angles in order from least to greatest: 45 < 67 < 68 Put in the missing sides from angle descriptions: clarinet < flute < trumpet

10. Ch 5 Coordinate Relations and Transformations • SSM: • any two sides greater than third Add two shortest and compare with longest, if greater then triangle 6 + 8 = 14 not > 14 no triangle 9 + 11 = 20 not > 21 no triangle 8.5 + 10.5 = 19 > 17 triangle 4.7 + 4.7 = 9.4 not > 14 no triangle

11. Ch 5 Triangles • SSM: • No help if not to scale • Measure sides with ruler Find missing angle: 180 –(64+54) = 62. Largest side (Rector) opposite largest angle. Smallest side (Taylor) opposite smallest angle.

12. Ch 5 Triangles • SSM: • no help Third side is found by Lg – sm < d < Lg + sm 84 – 63 < d < 84 + 63 21 < d < 147

13. Ch 5 Triangles • SSM: • draw figure and label • cover up given, one at a time, in order R S T Order numbers from smallest to largest: 10 < 14 < 16 Replace with segment (side) names: ST < RS < TR Find missing letter (opposite angle) R < T < S