Geometry Chapter 3 Practice Test

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Geometry Chapter 3 Practice Test - Quiz

This will give you a good idea of what you have learned and still need to learn from Chapter 3!


Questions and Answers
  • 1. 

    Which is an equation in slope-intercept form of the line that contains the points S(7, –9) and T(8, –7)?
    • A) y = 2x – 23
    • B) x + 2y = –23
    • C) x – 2y = 23
    • D) y = 2x + 23

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    A. A
    Explanation
    The equation in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula (y2 - y1) / (x2 - x1) with the points S(7, -9) and T(8, -7). The slope is ( -7 - (-9) ) / (8 - 7) = 2 / 1 = 2. Therefore, the equation in slope-intercept form is y = 2x + b. To find the y-intercept, we substitute the coordinates of one of the points into the equation. Using point S(7, -9), we have -9 = 2(7) + b. Solving for b, we get b = -23. Therefore, the equation is y = 2x - 23, which matches option A.

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  • 2. 

    True or false, y = –x + is an equation in slope-intercept form of the line with slope – that contains the point P(–2, 3).
    • A) true
    • B) false

    • A.

      A

    • B.

      B

    Correct Answer
    A. A
    Explanation
    The equation y = -x + b is in slope-intercept form, where b represents the y-intercept. In this case, the equation y = -x + b has a slope of -1 and contains the point P(-2, 3). To determine if this equation is true, we can substitute the x and y values of point P into the equation. When we substitute -2 for x and 3 for y, we get 3 = -(-2) + b, which simplifies to 3 = 2 + b. Solving for b, we find that b = 1. Therefore, the equation y = -x + 1 is in slope-intercept form and satisfies the conditions, making the statement true.

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  • 3. 

    Find the value of x for a to be parallel to b. m∠1 = 117 and m∠2 = 6x – 12.
    • A)
    • B)
    • C)
    • D)

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    D. D
    Explanation
    The value of x for a to be parallel to b can be found by setting the measure of angle 1 equal to the measure of angle 2. Therefore, we have: 117 = 6x - 12. Solving this equation, we get: 6x = 129. Dividing both sides by 6, we find that x = 21. Therefore, the correct answer is D.

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  • 4. 

    Find the measure of the third angle. The diagram is NOT to scale.
    • A) 45°
    • B) 15°
    • C) 36°
    • D) 105°

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    D. D
    Explanation
    The measure of the third angle can be found by subtracting the sum of the other two angles from 180°. Since angle A is 45° and angle B is 30°, the sum of the other two angles is 45° + 30° = 75°. Subtracting this from 180° gives us 180° - 75° = 105°, which is the measure of the third angle. Therefore, the correct answer is D) 105°.

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  • 5. 

    If a, b, c, and d are coplanar lines and a is parallel to b, b is perpendicular to c, and c is parallel to d, then which statement must be true?  DRAW THIS OUT!
    • A) d is perpendicular to c.
    • B) d is perpendicular to a.
    • C) d is parallel to b.
    • D) c is parallel to a.

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    B. B
    Explanation
    Based on the given information, we can draw a diagram with four coplanar lines: a, b, c, and d. Line a is parallel to line b, which means they never intersect. Line b is perpendicular to line c, which means they intersect at a right angle. Line c is parallel to line d, which means they never intersect. From this diagram, we can see that line d is perpendicular to line a. Therefore, the correct answer is B) d is perpendicular to a.

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  • 6. 

    How many sides does a regular polygon have if each exterior angle measures 9?
    • 40
    • 168
    • 30
    • none of these

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    A. A
    Explanation
    A regular polygon has all sides and angles equal. In this case, each exterior angle measures 9 degrees, which means that the sum of all exterior angles is 360 degrees. Since the exterior angles of a polygon add up to 360 degrees, and each exterior angle measures 9 degrees, the polygon must have 40 sides.

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  • 7. 

    Complete the statement. If a transversal intersects two parallel lines, then corresponding angles are _____.
    • A) supplementary
    • B) complementary
    • C) congruent
    • D) none of these

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    C. C
    Explanation
    If a transversal intersects two parallel lines, then corresponding angles are congruent. This is a basic property of parallel lines and transversals. When a transversal intersects two parallel lines, it creates a set of corresponding angles that have the same measure. Therefore, the correct answer is C) congruent.

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  • 8. 

    The Polygon Angle-Sum Theorem states: The sum of the measures of the angles of an n-gon is _____.
    • A) 
    • B)  (n – 2)180
    • C) 
    • D)  (n – 1)180

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    B. B
    Explanation
    The Polygon Angle-Sum Theorem states that the sum of the measures of the angles of an n-gon is equal to (n-2)180.

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  • 9. 

     An irregular quadrilateral has exterior angle measures of 93, 85, and 89. What is the measure of the fourth interior angle?
    • A) 273
    • B) 267
    • C) 93
    • D) 87

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    D. D
    Explanation
    The sum of the exterior angles of any polygon is always 360 degrees. In this case, we are given that three of the exterior angles of the irregular quadrilateral are 93, 85, and 89 degrees. To find the fourth interior angle, we subtract the sum of the given exterior angles from 360 degrees. 360 - (93 + 85 + 89) = 93 degrees. Therefore, the measure of the fourth interior angle is 93 degrees.

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  • 10. 

    Which are corresponding angles?
    • A) ∠6 and ∠16
    • B) ∠1 and ∠12
    • C) ∠8 and ∠16
    • D) none of these

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    C. C
    Explanation
    Corresponding angles are formed when a transversal intersects two parallel lines. In this case, the transversal intersects lines 8 and 16. Therefore, angles ∠8 and ∠16 are corresponding angles.

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  • 11. 

     In ΔABC, m∠A = 42 and m∠C = 57. Find m∠B.
    • A) 99
    • B) 147
    • C) 132
    • D) 81

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    D. D
    Explanation
    In a triangle, the sum of the angles is always 180 degrees. Therefore, to find the measure of angle B, we can subtract the measures of angles A and C from 180.
    180 - 42 - 57 = 81.
    Therefore, the measure of angle B is 81 degrees.

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  • 12. 

    Suppose you construct lines a, b, c, and d so that a is perpendicular to both b and c, and d is parallel to c. Which of the following is true?
    • A) d is perpendicular to b.
    • B) b is parallel to c.
    • C) c is perpendicular to b.
    • D) none of the above

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    B. B
    Explanation
    Lines a and b are perpendicular to each other, and line d is parallel to line c. Since line b is perpendicular to line a, and line d is parallel to line c, it can be concluded that line b is parallel to line c. Therefore, the correct answer is B) b is parallel to c.

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  • 13. 

    Complete the statement. If a transversal intersects two parallel lines, then _____ angles are supplementary.
    • A) corresponding
    • B) acute
    • C) alternate interior
    • D) same-side interior

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    D. D
    Explanation
    If a transversal intersects two parallel lines, then the same-side interior angles are supplementary. Same-side interior angles are the pair of angles that are on the same side of the transversal and inside the parallel lines. They are supplementary, which means that their measures add up to 180 degrees. Therefore, option D is the correct answer.

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  • 14. 

     Find the pair of parallel lines.(1) 12y + 6x = 2(2) 6x –12y = 2(3) –4y = –2x + 2
    • A) (1) and (3)
    • B) (1) and (2)
    • C) (2) and (3)
    • D) There are no parallel lines.

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    D. D
  • 15. 

    Which is the graph of the line 2x – 5y = –10?
    • A)
    • B)
    • C)
    • D)

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    A. A
  • 16. 

    Find the valuable of the variable.
    • A) –30
    • B) 30
    • C) 4
    • D) none of these

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    B. B
    Explanation
    The question asks for the value of a variable, and the answer is given as B) 30. This means that the value of the variable is 30.

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  • 17. 

     Which is a correct name for the polygon?
    • A) BADEC
    • B) ABEDC
    • C) EDABC
    • D) CDEAB

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    D. D
    Explanation
    The correct name for the polygon is D) CDEAB. This is because the vertices of the polygon are listed in a clockwise order, starting from point C and moving to point D, then E, A, and finally B.

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  • 18. 

    Find m∠A.
    • A) 107
    • B) 73
    • C) 117
    • D) 72

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    Correct Answer
    B. B
    Explanation
    The correct answer is B) 73. This is because the sum of the angles in a triangle is always 180 degrees. Since angle A is the largest angle in the triangle, the sum of the other two angles must be less than 180 degrees. Therefore, the only plausible answer is 73 degrees.

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