Similarity, congruence and Proofs (unit 2) Name Similarity, congruence and Proofs (unit 2) Name: 1

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  • Similarity, congruence and Proofs (unit 2) Name:

    1. If the sum of the measures of two angles is 90◦, then the angles are complementary. In triangle ABC, m∠A = 25◦, m∠B = 65◦, m∠C = 90◦.

    Which valid conclusion follows directly from the previous statements?

    A. ∠C is a complementary angle.

    B. ∠B and ∠C are complementary angles.

    C. ∠A and ∠C are complementary angles.

    D. ∠A and ∠B are complementary angles.

    2. Which is a true statement about angles 1 and 2 shown below?

    A. ∠1 is complementary to ∠2. B. ∠1 is supplementary to ∠2.

    C. Both angles are obtuse. D. Both angles are acute.

    3. The diagram below shows angles formed by intersecting lines.

    Which answer reflects the relationship between ∠2 and ∠3?

    A. ∠2 and ∠3 are vertical angles.

    B. ∠2 and ∠3 are corresponding angles.

    C. ∠2 and ∠3 are alternate exterior angles.

    D. ∠2 and ∠3 are adjacent supplementary angles.

    4. Which term describes ∠1 and ∠2?

    A. supplementary B. complementary

    C. vertical D. congruent

    5. Which of the following is a pair of supplementary angles?

    A. ∠BOF and ∠BOA B. ∠COD and ∠DOE

    C. ∠COF and ∠AOF D. ∠DOE and ∠DOB

    page 1

  • 6. In which figure is the measure of ∠1 not equal to 60◦ ?

    A.

    B.

    C.

    D.

    7. Use the figure below to answer the following question.

    Which word describes the relationship between ∠1 and ∠2?

    A. acute B. complementary

    C. obtuse D. supplementary

    8. Which angles are complementary?

    A. ∠2 and ∠3 B. ∠3 and ∠4 C. ∠4 and ∠5 D. ∠1 and ∠2

    9. A diagram is shown below.

    Which angle must be congruent to ∠AGB?

    A. ∠DGE B. ∠EGA C. ∠AGF D. ∠CGD

    10. What is the measure, in degrees, of the angle that is complementary to ∠RVS?

    A. 30◦ B. 60◦ C. 90◦ D. 110◦

    11. What is the measure of angle 1 in the figure below?

    A. 30◦ B. 40◦ C. 60◦ D. 80◦

    page 2 Similarity, congruence and Proofs (unit 2)

  • 12. In the figure below, ←→ CD intersects

    ←→ AB at F, m∠CFB = 50◦, and

    ∠EFA ∼= ∠AFD. What is m∠EFC ?

    A. 40◦ B. 50◦ C. 70◦ D. 80◦

    13. Julia is taking pictures with a digital camera on a tripod. She plans to make a 360◦ panorama using a photo software application. The lens on her camera allows her to take pictures that will measure 78◦, as shown.

    If she takes the pictures with a 10◦ overlap, how many pictures will need to be taken to make a 360◦ panorama?

    14. A straight line measures 180◦. A straight line and a triangle are touching as shown in the figure below.

    What is the value of x in the figure?

    A. 64 B. 84 C. 90 D. 96

    15. Angles F and G are complementary angles. Angles G and H are supplementary angles. The degree measure of each angle is a whole number. What is the smallest possible measure of angle H?

    A. 1◦ B. 89◦ C. 91◦ D. 179◦

    16. Use the figure below to answer the question.

    What is the value of x?

    A. 39◦ B. 48◦ C. 51◦ D. 81◦

    17. The figure below shows two intersecting lines.

    Based on the given angle measure, what is the value of x?

    18. Line g intersects line h in the figure below.

    Based on the angle measure given in the figure, what is the value of x?

    A. 30 B. 60 C. 100 D. 120

    page 3 Similarity, congruence and Proofs (unit 2)

  • 19. Angle XYZ is a 180◦ angle. Angle XYZ is divided into three smaller angles, as shown below.

    What is the measure of angle XYP?

    A. 35◦ B. 45◦ C. 55◦ D. 125◦

    20. Triangle PQR, triangle RST , and two angle measures are shown below.

    Line segment QT intersects line segment PS at point R.

    What is the value of x?

    21. Use the figure below to answer the following question.

    Angle A measures 124◦. What is the measure of an angle that is supplementary to angle A?

    A. 34◦ B. 56◦ C. 66◦ D. 236◦

    22. The figure shows supplementary angles.

    What is the measure of angle D?

    A. 45◦ B. 135◦ C. 180◦

    23. Look at the angles formed by the intersecting lines.

    Which angles must be congruent?

    A. ∠2 and ∠7 B. ∠4 and ∠6 C. ∠5 and ∠8 D. ∠3 and ∠6

    24. When a marble hits a wall, it bounces off the wall at the same angle it hits the wall.

    If a marble hits a wall at a 22 degree angle, what is the measure of the angle between the two paths of the marble?

    A. 44◦ B. 68◦ C. 136◦ D. 158◦

    page 4 Similarity, congruence and Proofs (unit 2)

  • 25. What is the value of x in the figure below if L1 is parallel to L2?

    A. x = 911 B. x = 165 9 11 C. x = 9 D. x = −9

    26. In the figure below, −−→ BD intersects

    ←→ AC at point B.

    What is the measure of ∠ABD?

    A. 68◦ B. 112◦ C. 124◦ D. 170◦

    27. If the two rays are perpendicular, what is the value of m?

    28. Line ` is parallel to line m. Line t is a transversal with angle measures as indicated below.

    Note: The figure is not drawn to scale.

    What is the value of x?

    A. 16 B. 20 C. 25 D. 32

    29. In the diagram below, lines p and q are parallel, and line t is the transversal.

    What is the value of x ?

    A. 50 B. 70 C. 90 D. 110

    30. −−→ OB bisects ∠AOC. If m∠AOB = (3x + 16) and m∠BOC = (8x − 14), what is m∠AOB?

    A. 18 B. 26 C. 34 D. 48

    page 5 Similarity, congruence and Proofs (unit 2)

  • 31. −−− SU intersects

    −−− TV at point R. What is the value of x, in degrees?

    32. In the diagram below, ∠HDA and ∠ADR are supplementary.

    What is the value of x?

    A. 21 B. 18 C. 11 D. 9

    33. In the figure shown below, lines j and k are parallel.

    Which equation can be used to find the value of x in the figure?

    A. (x + 40) = (2x + 20) B. 2(x + 40) = 2x + 20

    C. (x + 40) + (2x + 20) = 90 D. (x + 40) + (2x + 20) = 180

    34. In the figure below, lines A and B are straight and parallel to each other.

    Which angles must be congruent to ∠1?

    A. ∠2 and ∠6 B. ∠3 and ∠5

    C. ∠4, ∠6, and ∠7 D. ∠4, ∠5, and ∠8

    35. If two parallel lines are cut by a nonperpendicular transversal, which type of angles are not congruent?

    A. corresponding angles B. alternate interior angles

    C. alternate exterior angles D. same-side interior angles

    36. In the diagram below, transversal t intersects parallel lines m and n.

    Which of the following angles is not congruent to ∠A?

    A. ∠3 B. ∠5 C. ∠7 D. ∠8

    page 6 Similarity, congruence and Proofs (unit 2)

  • 37. A transversal crosses two parallel lines. Which statement should be used to prove that the measures of angles 1 and 5 sum to 180◦?

    A. Angles 1 and 8 are congruent as corresponding angles; angles 5 and 8 form a linear pair.

    B. Angles 1 and 2 form a linear pair; angles 3 and 4 form a linear pair.

    C. Angles 5 and 7 are congruent as vertical angles; angles 6 and 8 are congruent as vertical angles.

    D. Angles 1 and 3 are congruent as vertical angles; angles 7 and 8 form a linear pair.

    38. In the diagram below, lines x, y, and z are all parallel, and lines r and s intersect at line y.

    Which equation must be true?

    A. m∠1 = 180◦ − m∠7 B. m∠2 = 90◦ + m∠5

    C. m∠3 + m∠4 = m∠7 D. m∠5 + m∠6 = m∠7

    39. Parallel lines r and s are cut by transversal t, as shown in the diagram below.

    Which of the following must be true?

    A. m∠1 + m∠5 = 180◦ B. m∠2 + m∠8 = 180◦

    C. m∠1 = m∠7 D. m∠3 = m∠8

    40. In the diagram below, m ‖ q. Line w intersects lines m and q.

    Which of the following are corresponding angles?

    A. ∠2 and ∠5 B. ∠5 and ∠7 C. ∠7 and ∠1 D. ∠1 and ∠2

    page 7 Similarity, congruence and Proofs (unit 2)

  • 41. In the diagram below, ∠1 ∼= ∠4.

    Which of the following conclusions does not have to be true?

    A. ∠3 and ∠4 are supplementary angles.

    B. Line l is parallel to line m.

    C. ∠1 ∼= ∠3

    D. ∠2 ∼= ∠3

    42. Use the proof to answer the question below.

    Given: ∠2 ∼= ∠3

    Prove: ∠1 ∼= ∠4

    Statement Reason

    ∠2 ∼= ∠3 1. Given ∠1 ∼= ∠2; ∠3 ∼= ∠4 2. ? ∠1 ∼= ∠4 3. Transitive Property

    What reason can be used to justify statement 2?

    A. Complements of congruent angles are congruent.

    B. Vertical angles are congruent.

    C. Supplements of congruent angles are congruent.

    D. Corresponding angles are congruent.

    43. Line AB, line CD, and line EF are shown below.

    Which statement describing a relationship between line AB and line CD must be true?

    A. The lines are parallel.

    B. The lines bisect each other.

    C. The lines are perpendicular.

    D. The lines intersect, forming acute angles.

    44. Given the diagram below, what information is needed to prove that the lines are parallel?

    A. m∠1 = m∠3 B. m∠1 = m∠6

    C. m∠1 = m∠7 D. m∠1 = m∠8

    page 8 Similarity, congruence and Proofs (unit 2)

  • 45. In the diagram below, line l is parallel to line m, and line k intersects both lines.

    Based on the angl

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