- 1. Which theorem states that if one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side?
A) Hinge Theorem or SAS Inequality Theorem
B) Triangle Inequality Theorem
C) Exterior Angle Inequality Theorem
- 2. In Triangle Inequality Theorem, which of the following describes the relationship of the sum of its two sides to its third length?
A) less than or equal to
B) greater than
C) greater than or equal to
- 3. Which of the following theorems on triangle inequalities states that the measure of an exterior angle of a triangle is greater than the measure of either remote interior angle?
A) Hinge Theorem or SAS Inequality Theorem
B) Angle-Side Relationship Theorem
C) Exterior Angle Inequality Theorem
- 4. Which of the following theorems deals with the two triangles whose two corresponding sides are congruent and whose included angle are unequal?
A) Exterior Nagle Inequality Theorem
B) SAS Inequality Theorem
C) SSS Inequality Theorem
- 5. Which of the following could NOT be used as the length of the sides of a triangle?
A) 3, 3, 3
B) 5, 7, 9
C) 4, 5, 10
- 6. Which of the following statements is FALSE?
A) The smallest side of a triangle is opposite to the smallest angle.
B) The largest angle of a triangle is opposite to the longest side.
C) Any lengths of the sides can be used to form a triangle.
- 7. If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second. Which of the following theorems pertains to two triangles whose two corresponding sides are congruent and whose third sides are unequal?
A) Triangle Inequality Theorem
B) Exterior Angle Inequality Theorem
C) Converse of Hinge Theorem or SSS Inequality Theorem
- 8. If two angles of a triangle are not congruent, then the larger side is opposite the larger angle.
A) Hinge Theorem or SAS Inequality Theorem
B) Angle-Side Relationship Theorem
C) Exterior Angle Inequality Theorem
- 9. The sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.
A) Exterior Angle Inequality Theorem
B) Angle-Side Relationship Theorem
C) Triangle Inequality Theorem
- 10. The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.
A) Triangle Inequality Theorem
B) Angle-Side Relationship Theorem
C) Exterior Angle Inequality Theorem
- 11. If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second.
A) Converse of Hinge Theorem or SSS Inequality Theorem
B) Triangle Inequality Theorem
C) Exterior Angle Inequality Theorem
- 12. 17, 16, 9 could be the lengths of a triangle
A) TRUE
B) FALSE
- 13. 1, 2, 3 could be the lengths of a triangle
A) FALSE
B) TRUE
- 14. 9, 11, 18 could be a lengths of a triangle
A) TRUE
B) FALSE
- 15. 4, 8, 11 could be the lengths of a triangle
A) TRUE
B) FALSE
- 16. 5, 13, 6 could be the lengths of a triangle
A) TRUE
B) FALSE
- 17. are two nonadjacent interior angles on opposite sides of the transversal.
A) Alternate Exterior Angles
B) Alternate Interior Angles
- 18. are two nonadjacent exterior angles on opposite sides of a transversal.
A) Alternate Interior Angles
B) Alternate Exterior Angles
- 19. are two nonadjacent angles, one interior, and one exterior on the same side of the transversal.
A) Alternate Interior Angles
B) Vertical Angle Theorem
C) Corresponding Angles
- 20. Two angles are vertical angles if and only if they are nonadjacent angles formed by two intersecting lines.
A) Vertical Angles
B) Corresponding Angles
C) Alternate Interior Angles
- 21. Through a point not on a line, you can sometimes construct a parallel line.
A) FALSE
B) TRUE
- 22. Two lines that are parallel to a third line are never parallel.
A) FALSE
B) TRUE
- 23. Two lines are parallel if they are coplanar and do not intersect.
A) TRUE
B) FALSE
- 24. Through a point outside a line, there is one and only one line parallel to the given line.
A) FALSE
B) TRUE
- 25. The shelves of a bookcase are parallel to each other.
A) FALSE
B) TRUE
- 26. Which is always true about the measure of an exterior angle of a triangle?
A) It is less than the measure of its adjacent interior angle.
B) It is less than the measure of either remote interior angle.
C) It is greater than the measure of either remote interior angle.
- 27. Carlos concluded that the longest side in ???????? is ???? opposite to ???? ???? after finding that the angle ???? is the largest angle. What theorem did Carlos use to make such conclusion?
A) Converse of Hinge Theorem or SSS Triangle Inequality Theorem
B) Triangle Inequality Theorem 2 (???? ? ????)
C) Triangle Inequality Theorem 1 (???? ? ????)
- 28. If one side of a triangle is longer than a second side, then the angle opposite the longer side is larger than the angle opposite the second side.
A) Triangle Inequality Theorem 1 (Ss ? Aa)
B) Triangle Inequality Theorem 2 (Aa?Ss)
C) Triangle Inequality Theorem 3 (S1+S2 > S3)
- 29. If one angle of a triangle is larger than a second angle, then the side opposite the larger angle is longer than the side opposite the second angle.
A) Triangle Inequality Theorem 3 (S1+S2 > S3)
B) Triangle Inequality Theorem 2 (Aa?Ss)
C) Triangle Inequality Theorem 1 (Ss ? Aa)
- 30. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
A) Triangle Inequality Theorem 2 (Aa?Ss)
B) Triangle Inequality Theorem 3 (S1+S2 > S3)
C) Triangle Inequality Theorem 1 (Ss ? Aa)
- 31. The following are inequalities for one triangle EXCEPT:
A) exterior angle inequality theorem
B) the hinge theorem
C) triangle inequality theorem
- 32. this allows to create the angluar degree
A) exterior
B) angle
C) hinge
- 33. The sum of the lengths of TWO SIDES of a triangle is _____ than the length of the third side.
A) equal
B) greater
C) lesser
- 34. a triangle has _____ angles.
A) one
B) two
C) three
- 35. is an angle which forms a linear pair (adjacent) with one of the triangle's interior angles.
A) exterior angle of a triangle
B) interior angle of a triangle
- 36. are two interior angles not adjacent to the exterior angles.
A) remote exterior angle
B) remote interior angles
- 37. The Triangle Inequality Theorem deals with _______ of a triangle
A) vertex
B) angles
C) sides
- 38. Name the smallest angle in this triangle.
A) ∠C
B) ∠A
C) ∠B
- 39. Does a triangle with these side lengths exist? 15, 12, 9
A) NO
B) YES
C) I do not know
- 40. Select the measurements that match the sides of a triangle.
A) 7, 12, 1
B) 7, 9, 19
C) 7, 7, 7
- 41. Two sides of a triangle have side lengths of 17 meters and 12 meters. What is the range of possible lengths for the third side?
A) 12 < x < 29
B) 12 < x < 17
C) 5 < x < 29
- 42. What is the smallest SIDE?
A) side PE
B) side EN
C) side PN
- 43. What is the longest SIDE?
A) side PN
B) side PE
C) side EN
- 44. are two nonadjacent interior angles on opposite sides of the transversal.
A) Alternate Interior Angles
B) Alternate Exterior Angles
- 45. It is called the HINGE theorem, because...
A) "hinge" is the Spanish word for angle.
B) the triangle makes a hinge shape, like a tent.
C) the vertex of the angle acts like a hinge to open the triangle.
- 46. Four students are doing a scavenger hunt starting at the water fountain. They disagree one the directions and split up. Their paths are shown in the diagram. Which pair is closest to the fountain when they stop?
A) Luther and Stephanie
B) Mario and Lee
- 47. Which is NOT a possible measure for ∠DCB?
A) 27º
B) 34º
C) 30º
D) 35º
- 48. Which of the following is a possible length for segment AC
A) 10
B) 15
C) 17
- 49. Select the correct answer
A) C
B) B
C) D
D) A
- 50. Using the hinge theorem, we can say that AB _____ DC
A) Greater than
B) Less than
C) Equal to
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