- 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) Triangle Inequality Theorem
B) Hinge Theorem or SAS 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) Angle-Side Relationship Theorem
B) Exterior Angle Inequality Theorem
C) Hinge Theorem or SAS 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) SSS Inequality Theorem
C) SAS Inequality Theorem
- 5. Which of the following could NOT be used as the length of the sides of a triangle?
A) 4, 5, 10
B) 5, 7, 9
C) 3, 3, 3
- 6. Which of the following statements is FALSE?
A) The smallest side of a triangle is opposite to the smallest angle.
B) Any lengths of the sides can be used to form a triangle.
C) The largest angle of a triangle is opposite to the longest side.
- 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) Exterior Angle Inequality Theorem
B) Triangle 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) Exterior Angle Inequality Theorem
C) Angle-Side Relationship 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) Triangle Inequality Theorem
C) Angle-Side Relationship 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) Exterior Angle Inequality Theorem
C) Angle-Side Relationship 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) Triangle Inequality Theorem
B) Exterior Angle Inequality Theorem
C) Converse of Hinge Theorem or SSS 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) TRUE
B) FALSE
- 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 Interior Angles
B) Alternate Exterior Angles
- 18. are two nonadjacent exterior angles on opposite sides of a transversal.
A) Alternate Exterior Angles
B) Alternate Interior Angles
- 19. are two nonadjacent angles, one interior, and one exterior on the same side of the transversal.
A) Corresponding Angles
B) Alternate Interior Angles
C) Vertical Angle Theorem
- 20. Two angles are vertical angles if and only if they are nonadjacent angles formed by two intersecting lines.
A) Corresponding Angles
B) Alternate Interior Angles
C) Vertical 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 greater than the measure of either remote interior angle.
B) It is less than the measure of either remote interior angle.
C) It is less than the measure of its adjacent 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) Triangle Inequality Theorem 2 (???? ? ????)
B) Converse of Hinge Theorem or SSS Triangle Inequality Theorem
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 3 (S1+S2 > S3)
B) Triangle Inequality Theorem 2 (Aa?Ss)
C) Triangle Inequality Theorem 1 (Ss ? Aa)
- 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 2 (Aa?Ss)
B) Triangle Inequality Theorem 3 (S1+S2 > S3)
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 3 (S1+S2 > S3)
B) Triangle Inequality Theorem 1 (Ss ? Aa)
C) Triangle Inequality Theorem 2 (Aa?Ss)
- 31. The following are inequalities for one triangle EXCEPT:
A) triangle inequality theorem
B) exterior angle inequality theorem
C) the hinge theorem
- 32. this allows to create the angluar degree
A) exterior
B) hinge
C) angle
- 33. The sum of the lengths of TWO SIDES of a triangle is _____ than the length of the third side.
A) lesser
B) equal
C) greater
- 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) interior angle of a triangle
B) exterior 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) angles
B) sides
C) vertex
- 38. Name the smallest angle in this triangle.
A) ∠A
B) ∠C
C) ∠B
- 39. Does a triangle with these side lengths exist? 15, 12, 9
A) I do not know
B) YES
C) NO
- 40. Select the measurements that match the sides of a triangle.
A) 7, 9, 19
B) 7, 12, 1
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) 5 < x < 29
C) 12 < x < 17
- 42. What is the smallest SIDE?
A) side PN
B) side EN
C) side PE
- 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 vertex of the angle acts like a hinge to open the triangle.
C) the triangle makes a hinge shape, like a tent.
- 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) 30º
B) 27º
C) 34º
D) 35º
- 48. Which of the following is a possible length for segment AC
A) 10
B) 17
C) 15
- 49. Select the correct answer
A) C
B) B
C) A
D) D
- 50. Using the hinge theorem, we can say that AB _____ DC
A) Greater than
B) Equal to
C) Less than
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