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Relationships of angles and sides

Relationships of angles and sides. To order the measures of the sides and angles of a triangle. To use triangle inequalities to solve problems. 1: Theorem: Alternate Interior Angles. If one side of a triangle is longer than another side,

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Relationships of angles and sides

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  1. Relationships of angles and sides To order the measures of the sides and angles of a triangle. To use triangle inequalities to solve problems.

  2. 1: Theorem: Alternate Interior Angles If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

  3. 2:Theorem : Same-Side Interior Angles If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

  4. Straws Cut segments of one straw into 3, 5, and 9 centimeters. Can you make a triangle?

  5. Straws Cut segments of one straw into 4, 5, and 7 centimeters. Can you make a triangle?

  6. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

  7. Which segment is shortest? RO

  8. Which segment is shortest? AY

  9. Find x. Which side is longest? X = 59 PE

  10. The perimeter is 51. Find x. Which angle is the smallest? X =10  D

  11. The perimeter is 22. Find x. Which angle is the largest? X =2 A

  12. Which side is opposite A in APK? PK

  13. Which angle is opposite AK in APK? P

  14. Which side is opposite R in QKR? QK

  15. Which angle is opposite KR in QKR?  Q

  16. The side opposite 1 in BKN is _____? KN

  17. The side opposite 1 in BJN is _____? JN

  18. The angle opposite NJ in JNY is _____? 6 orY

  19. What is the shortest, longest side ED can be? __<X<__ 13 43 15 X 28

  20. What is the shortest, longest side ED can be? __<X<__ 10 14 2 X 12

  21. What is the shortest, longest side PA can be? __<X<__ 24 40 X 32 8

  22. What is the shortest, longest side PA can be? __<X<__ 16 42 X 29 13

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