Geometry Chapter 5 Test (2024)

Table of Contents

Find the value of x and QA.x =QA = In , Z is the centroid, MZ = 6, YI = 18, and NZ = 12.MR =ZV =YZ = Point A is the incenter of . Find .= Find the range for the measure of the third side of a triangle given two sides with lengths 31 cm and 39 cm. List the sides of in least to greatest order Point P in the incenter of . If PY = 40 and JY = 32, find LP.LP = Is it possible to form a triangle with the given sides lengths of 4 ft, 8 ft, and 18 ft. If not explain why not. Find the range for the third side of a triangle given two sides with measures of 7 km and 29 km. Lines s, t, and u are perpendicular bisectors of the sides of and meet at J. If JG = 2x + 2, JH = 2y – 2,JF = 8, and HI = 2z – 3, find x, y, and z.x =y =z = In , CP = 30 EP = 18, and BF = 39. Find the value of each measurePD = __________________ PA = __________________FP = __________________CD = __________________EA = __________________BP = __________________ The point of concurrency of the perpendicular bisectors of a triangle and is equidistant from the vertices of a triangle. The point of concurrency of the angle bisectors of triangle and is equidistant from the sides of a triangle. The point of concurrency of the medians of a triangle and is two thirds of the distance form each vertex to the midpoint of the opposite side. In the diagram given, which angle has the greatest measure of .cannot be determined Which set of numbers cannot represent the lengths of the sides of a triangle? Determine the relationship between Determine the relationship between

1.
Find the value of x and QA.x =QA =
2.
In , Z is the centroid, MZ = 6, YI = 18, and NZ = 12.MR =ZV =YZ =
3.
Point A is the incenter of . Find .=
4.
Find the range for the measure of the third side of a triangle given two sides with lengths 31 cm and 39 cm.
5.
List the sides of in least to greatest order
6.
Point P in the incenter of . If PY = 40 and JY = 32, find LP.LP =
7.
Is it possible to form a triangle with the given sides lengths of 4 ft, 8 ft, and 18 ft. If not explain why not.
8.
Find the range for the third side of a triangle given two sides with measures of 7 km and 29 km.
9.
Lines s, t, and u are perpendicular bisectors of the sides of and meet at J. If JG = 2x + 2, JH = 2y – 2,JF = 8, and HI = 2z – 3, find x, y, and z.x =y =z =
10.
In , CP = 30 EP = 18, and BF = 39. Find the value of each measurePD = __________________ PA = __________________FP = __________________CD = __________________EA = __________________BP = __________________
11.
The point of concurrency of the perpendicular bisectors of a triangle and is equidistant from the vertices of a triangle.
- A.
  Centroid
- B.
  Incenter
- C.
  Orthocenter
- D.
  Circumcenter
- E.
  Nine-Point Center
Correct Answer
D. Circumcenter
Explanation
The circumcenter is the point of concurrency of the perpendicular bisectors of a triangle. It is equidistant from the vertices of the triangle, meaning that the distance from the circumcenter to each vertex is the same. This property makes the circumcenter the center of the circumcircle, which is a circle that passes through all three vertices of the triangle.
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12.
The point of concurrency of the angle bisectors of triangle and is equidistant from the sides of a triangle.
- A.
  Centroid
- B.
  Incenter
- C.
  Orthocenter
- D.
  Circumcenter
- E.
  Nine-Point Center
Correct Answer
B. Incenter
Explanation
The incenter of a triangle is the point of concurrency of the angle bisectors. It is the center of the inscribed circle, which is equidistant from all three sides of the triangle. Therefore, the given statement is true and the correct answer is "Incenter".
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11
13.
The point of concurrency of the medians of a triangle and is two thirds of the distance form each vertex to the midpoint of the opposite side.
- A.
  Centroid
- B.
  Incenter
- C.
  Orthocenter
- D.
  Circumcenter
- E.
  Nine-Point Center
Correct Answer
A. Centroid
Explanation
The centroid of a triangle is the point of concurrency of the medians. A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. The centroid is located two thirds of the distance from each vertex to the midpoint of the opposite side. Therefore, the correct answer is centroid.
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14.
In the diagram given, which angle has the greatest measure of .
4. cannot be determined
- A.
  A
- B.
  B
- C.
  C
- D.
  D
Correct Answer
A. A
Explanation
Without any additional information or measurements provided in the diagram, it is not possible to determine which angle has the greatest measure. Therefore, the correct answer is "cannot be determined".
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10
15.
Which set of numbers cannot represent the lengths of the sides of a triangle?
- A.
  6, 8, 11
- B.
  5, 6, 7
- C.
  7, 11, 18
- D.
  9, 12, 19
Correct Answer
C. 7, 11, 18
Explanation
In order for a set of numbers to represent the lengths of the sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In the given set, the sum of the lengths of the two smaller sides (7 and 11) is equal to the length of the longest side (18), violating the triangle inequality theorem. Therefore, the set 7, 11, 18 cannot represent the lengths of the sides of a triangle.
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10
16.
Determine the relationship between
- A.
  M∠RST=m∠TRS
- B.
  M∠RST
- C.
  M∠RST>m∠TRS
- D.
  No relationship
Correct Answer
C. M∠RST>m∠TRS
Explanation
The given answer states that m∠RST is greater than m∠TRS. This implies that the measure of angle RST is larger than the measure of angle TRS.
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17.
Determine the relationship between
- A.
  DH = GH
- B.
  DH < GH
- C.
  DH > GH
- D.
  No relationship
Correct Answer
C. DH > GH
Explanation
The given answer states that DH is greater than GH. This implies that DH is larger or has a higher value than GH.
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