Test Your Skills On Geometry Quiz

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    In the triangles above, what is the value of X? - ProProfs

    In the triangles above, what is the value of X?

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About This Quiz

Test your skills on geometry with this engaging quiz. Explore various aspects like triangle angles, supplementary angles, properties of rhombuses, and theorems like the Parallel Postulate. Ideal for learners seeking to deepen their understanding of geometric principles and their applications.

Test Your Skills On Geometry Quiz - Quiz

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  • 2. 

    The supplementary angle of 175 degrees is acute.

    • True

    • False

    Correct Answer
    A. False
    Explanation
    A supplementary angle is defined as one of two angles that add up to 180 degrees. Given that 175 degrees is already very close to 180 degrees, its supplementary angle would be very small (5 degrees). An acute angle is defined as an angle that measures less than 90 degrees. Since the supplementary angle of 175 degrees is only 5 degrees, it is not an acute angle.

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  • 3. 

    To PROVE that the sum of the angles inside a triangle is always 180 degrees, what two theorems or postulates will help you out?

    • The Parallel Postulate and The Alternate Interior Angles Theorem

    • Ceva's Theorem and The Parallel Postulate

    • The Alternate Interior Angles Theorem and Ceva's Theorem

    Correct Answer
    A. The Parallel Postulate and The Alternate Interior Angles Theorem
    Explanation
    The Parallel Postulate states that if a transversal intersects two parallel lines, then the alternate interior angles are congruent. This theorem helps in proving that the sum of the angles inside a triangle is always 180 degrees because it establishes the relationship between the alternate interior angles.

    The Alternate Interior Angles Theorem states that if a transversal intersects two lines and the alternate interior angles are congruent, then the lines are parallel. This theorem also helps in proving that the sum of the angles inside a triangle is always 180 degrees because it provides a way to establish the parallelism of lines.

    By using both the Parallel Postulate and the Alternate Interior Angles Theorem, one can prove that the sum of the angles inside a triangle is always 180 degrees.

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  • 4. 

    In the video, are the triangles in part B similar?  Choose all that apply.

    • No, because we only can find two angles.

    • Yes, because we can find two parallel lines.

    • Yes, because the triangles look similar.

    Correct Answer
    A. No, because we only can find two angles.
    Explanation
    The correct answer is "No, because we only can find two angles." This is because in order for two triangles to be similar, all corresponding angles must be equal. However, in this case, the statement mentions that we can only find two angles, which means that we cannot determine if all corresponding angles are equal. Therefore, we cannot conclude that the triangles in part B are similar.

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  • 5. 

    The angle bisectors of a rhombus are always ____________.

    Correct Answer
    Perpendicular
    Perpendicular bisectors
    Explanation
    The angle bisectors of a rhombus are always perpendicular because a rhombus has four equal sides and opposite angles that are congruent. The angle bisectors of a rhombus intersect at the center of the rhombus, forming right angles. Therefore, the angle bisectors are always perpendicular. Additionally, the perpendicular bisectors of the sides of a rhombus are also perpendicular since the sides of a rhombus are equal in length.

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  • 6. 

    Extra Credit:  In the creation of a 9-point circle, which of the following are NOT used in its construction?

    • The midpoint of each side of the triangle

    • The intersection point of each angle bisector and its opposite side

    • The foot of each altitude

    Correct Answer
    A. The intersection point of each angle bisector and its opposite side
    Explanation
    The 9-point circle is constructed using the midpoint of each side of the triangle and the foot of each altitude. The intersection point of each angle bisector and its opposite side is not used in its construction.

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  • 7. 

    Explain why the Parallel Postulate does not hold true in hyperbolic geometry.

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  • Current Version
  • Aug 29, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • May 10, 2011
    Quiz Created by
    Sethrocabra
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