Geometry Chapter 4 Test (4.1 To 4.6)

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| By Philip Benanti
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Philip Benanti
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Quizzes Created: 18 | Total Attempts: 26,587
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Geometry Chapter 4 Test (4.1 To 4.6) - Quiz

STANDARDS:G. CO. 12  G. CO. 10  G. CO. 7  G. SRT. 5  G. CO. 6  G. GPE. 4


Questions and Answers
  • 1. 

    • A.

      25

    • B.

      50

    • C.

      60

    • D.

      105

    Correct Answer
    D. 105
  • 2. 

    x = AB =BC =AC =

    Correct Answer
    N/A
  • 3. 

    x =m<1=

    Correct Answer
    N/A
  • 4. 

    Find the measures of the anglesm<1 =m<2 =m<3 =

    Correct Answer
    N/A
  • 5. 

    Find the measures of the anglesm<2 =m<3 =

    Correct Answer
    N/A
  • 6. 

    The measures of the angles of a triangle are 40°, 45°, and 95°.  The triangle is:

    • A.

      Obtuse

    • B.

      Right

    • C.

      Acute

    • D.

      Equilateral

    Correct Answer
    A. Obtuse
    Explanation
    The sum of the angles of a triangle is always 180 degrees. In this case, the sum of the given angles (40° + 45° + 95°) is 180°, which means it is a valid triangle. Since one of the angles (95°) is greater than 90°, the triangle is classified as obtuse.

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  • 7. 

    • A.

      Angle S is congruent to Angle A

    • B.

      Segment SN is congruent to Segment TN

    • C.

      Angle T is congruent to Angle U

    • D.

      Segment SU is congruent to Segment TN

    Correct Answer
    B. Segment SN is congruent to Segment TN
  • 8. 

    • A.

      Triangle CDE

    • B.

      Triangle DEC

    • C.

      Triangle ECD

    • D.

      Triangle EDC

    Correct Answer
    D. Triangle EDC
  • 9. 

    Use the diagram to solve for x

    • A.

      27

    • B.

      64

    • C.

      38

    • D.

      40

    Correct Answer
    A. 27
  • 10. 

    State the postulate or theorem that proves the two triangles are congruent.  (Mark the diagram) 

    • A.

      SSS

    • B.

      SAS

    • C.

      ASA

    • D.

      AAS

    Correct Answer
    A. SSS
    Explanation
    The correct answer is SSS. According to the Side-Side-Side (SSS) postulate, if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In the given diagram, the three sides of the triangles are congruent, which satisfies the SSS postulate and proves the triangles are congruent.

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  • 11. 

    State the postulate or theorem that proves the two triangles are congruent.  (Mark the diagram)

    • A.

      SSS

    • B.

      SAS

    • C.

      ASA

    • D.

      AAS

    Correct Answer
    D. AAS
    Explanation
    The postulate or theorem that proves the two triangles are congruent is the AAS (Angle-Angle-Side) postulate. According to this postulate, if two angles and the non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the two triangles are congruent. In the given diagram, if we have two angles in one triangle that are congruent to two angles in another triangle, and the non-included side between these angles is also congruent, then we can conclude that the triangles are congruent by the AAS postulate.

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  • 12. 

    If you are told that C is the midpoint of  and  which postulates and theorems would you need to use in order to prove that   Mark the diagram!

    • A.

      SAS, CPCTC, and then if alternate interior angles are congruent, lines are parallel

    • B.

      ASA, CPCTC, and then if corresponding angles are congruent, lines are parallel

    • C.

      SSS, CPCTC, and then if alternate interior angles are congruent, lines are parallel

    • D.

      HL, CPCTC, and then if corresponding angles are congruent, lines are parallel

    Correct Answer
    A. SAS, CPCTC, and then if alternate interior angles are congruent, lines are parallel
    Explanation
    The correct answer is SAS, CPCTC, and then if alternate interior angles are congruent, lines are parallel. This is because the given information states that C is the midpoint of AB, which implies that AC=CB. This satisfies the SAS (Side-Angle-Side) criterion for congruence. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can then be used to show that corresponding angles in the congruent triangles are congruent. Finally, if alternate interior angles are congruent, it implies that the lines are parallel.

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  • 13. 

    RS  =  2x + 6, RT  =  2x + 4, RQ  =  3x – 2, and RP  =  3x – 1, If , then the congruent segments are:  ______  and  ______Find the value of x.x =

    Correct Answer
    N/A

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Nov 23, 2014
    Quiz Created by
    Philip Benanti
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