Geometry Ch 15 Quiz

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  • 1/15 Questions

    What is line AD to the triangle?

    • Median
    • Angle bisector
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About This Quiz

The 'Geometry Ch 15 Quiz' assesses understanding of triangle properties, focusing on terms like median, concurrent lines, and altitude. It enhances comprehension of geometric principles crucial for academic progress in mathematics.

Geometry Quizzes & Trivia

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  • 2. 

    What is line AD to the triangle?

    • Median

    • Altitude

    Correct Answer
    A. Median
    Explanation
    Line AD is the median of the triangle. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. In this case, line AD connects vertex A to the midpoint of side BC. Medians are important in triangles as they intersect at a point called the centroid, which divides each median into two segments in a 2:1 ratio. The centroid is also the center of gravity of the triangle.

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  • 3. 

    An orthocenter is the point of concurrency of the lines containing the ______.

    Correct Answer
    altitudes
    Explanation
    The orthocenter is the point where the altitudes of a triangle intersect. An altitude is a line segment drawn from a vertex of the triangle perpendicular to the opposite side. Therefore, the correct answer is altitudes.

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  • 4. 

    What is the term for a line, segment, or ray that is perpenicular to the segment at its midpoint?

    • Perpendicular distance

    • Perpendicular bisector

    Correct Answer
    A. Perpendicular bisector
    Explanation
    A perpendicular bisector is a line, segment, or ray that intersects a given segment at its midpoint and forms a right angle with it. It divides the segment into two equal parts and is equidistant from the endpoints of the segment. This term is commonly used in geometry to describe a line that cuts another line into two equal halves at a right angle.

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  • 5. 

    Angle Bisector Theorem: If a point is on the ______ of an angle, then the point is equidistant from the _____ of the angle.

    Correct Answer
    bisector; sides
    Explanation
    The Angle Bisector Theorem states that if a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. In other words, if a line divides an angle into two equal angles, any point on that line will be the same distance away from each of the two sides of the angle.

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  • 6. 

    What is the red line to the triangle?

    • Median

    • Altitude

    • Angle bisector

    Correct Answer
    A. Altitude
    Explanation
    The red line to the triangle is an altitude. An altitude is a line segment that extends from a vertex of a triangle perpendicular to the opposite side. It can be used to find the height or distance from a vertex to the base of the triangle.

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  • 7. 

    What term means three or more lines that meet in one point?

    • Perpendicular bisector

    • Concurrent lines

    Correct Answer
    A. Concurrent lines
    Explanation
    Concurrent lines refer to three or more lines that intersect at a common point. This point of intersection is known as the point of concurrency. Therefore, concurrent lines are the correct term for three or more lines that meet in one point.

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  • 8. 

    What is the term for the point of concurrency of the medians?

    • Circumcenter

    • Point of concurrency

    • Orthocenter

    • Centroid

    Correct Answer
    A. Centroid
    Explanation
    The term for the point of concurrency of the medians is the centroid. The centroid is the point where all three medians of a triangle intersect. It is also known as the center of gravity of the triangle, as it is the balance point of the triangle's mass. The centroid divides each median into two segments, with the length of the segment from the vertex to the centroid being twice as long as the segment from the centroid to the midpoint of the opposite side.

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  • 9. 

    Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is ______ from the _______ of the segment. **This theorem does not work on ordinary BISECTORS and LINES.

    Correct Answer
    equidistant; endpoints
    Explanation
    The Perpendicular Bisector Theorem states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. In other words, the distance from the point to each endpoint of the segment is equal. This theorem is specifically applicable to perpendicular bisectors, which are lines that intersect the given segment at a right angle and divide it into two equal halves. It does not apply to ordinary bisectors or lines that are not perpendicular to the segment.

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  • 10. 

    What is the term for the point of concurrency of the perpendicular bisectors of the sides of a triangle?

    • Circumcenter

    • Incenter

    • Centroid

    • Orthocenter

    Correct Answer
    A. Circumcenter
    Explanation
    The term for the point of concurrency of the perpendicular bisectors of the sides of a triangle is the circumcenter. The circumcenter is the center of the circumcircle, which is a circle that passes through all three vertices of the triangle. It is the point equidistant from all three vertices, and the perpendicular bisectors of the sides intersect at this point.

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  • 11. 

    What is the term for the point of concurrency of the angle bisectors of a triangle?

    • Circumcenter

    • Centroid

    • Incenter

    • Orthocenter

    Correct Answer
    A. Incenter
    Explanation
    The incenter is the point of concurrency of the angle bisectors of a triangle. The angle bisectors of a triangle are the lines that divide each angle into two equal parts. The incenter is the center of the inscribed circle in the triangle, which is the largest circle that can fit inside the triangle.

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  • 12. 

    What is line DE to the triangle?

    • Midsegment

    • Median

    • Bisector

    Correct Answer
    A. Midsegment
    Explanation
    The line DE is the midsegment of the triangle. A midsegment is a line segment that connects the midpoints of two sides of a triangle. In this case, DE connects the midpoints of two sides of the triangle, making it the midsegment.

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  • 13. 

    Triangle Midsegment Theorem: If a segment joins the _______ of ___ sides of a triangle, then the segment is parallel to the ___ side and is ___ its length.

    Correct Answer
    midpoints; two; third; half
    Explanation
    The Triangle Midsegment Theorem states that if a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half its length. In this case, the correct answer states that the segment joins the midpoints of two sides of a triangle, making it parallel to the third side, and its length is half the length of the third side.

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  • 14. 

    What term describes the point at which concurrent lines meet?

  • 15. 

    What is the term for the distance from a point to a line: the length of the perpendicular segment from the point to the line?

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  • Current Version
  • Mar 20, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Nov 30, 2011
    Quiz Created by
    Carmendianne97
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