Geometry Ch 15 Quiz
Questions and Answers
- 1.
What is line AD to the triangle?
- A.
Median
- B.
Altitude
Correct Answer
A. MedianExplanation
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.Rate this question:
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- 2.
What term means three or more lines that meet in one point?
- A.
Perpendicular bisector
- B.
Concurrent lines
Correct Answer
B. Concurrent linesExplanation
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.Rate this question:
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- 3.
What term describes the point at which concurrent lines meet?
- 4.
What is line DE to the triangle?
- A.
Midsegment
- B.
Median
- C.
Bisector
Correct Answer
A. MidsegmentExplanation
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.Rate this question:
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- 5.
What is the red line to the triangle?
- A.
Median
- B.
Altitude
- C.
Angle bisector
Correct Answer
B. AltitudeExplanation
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.Rate this question:
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- 6.
What is line AD to the triangle?
- A.
Median
- B.
Angle bisector
Correct Answer
B. Angle bisectorExplanation
Line AD is an angle bisector in the triangle. An angle bisector is a line that divides an angle into two equal parts. In this case, line AD divides one of the angles in the triangle into two equal angles. This means that line AD cuts through the angle and splits it into two smaller angles of equal measure. Therefore, line AD is an angle bisector in the triangle.Rate this question:
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- 7.
What is the term for a line, segment, or ray that is perpenicular to the segment at its midpoint?
- A.
Perpendicular distance
- B.
Perpendicular bisector
Correct Answer
B. Perpendicular bisectorExplanation
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.Rate this question:
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- 8.
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; halfExplanation
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.Rate this question:
- 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; endpointsExplanation
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.Rate this question:
- 10.
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?
- 11.
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; sidesExplanation
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.Rate this question:
- 12.
What is the term for the point of concurrency of the perpendicular bisectors of the sides of a triangle?
- A.
Circumcenter
- B.
Incenter
- C.
Centroid
- D.
Orthocenter
Correct Answer
A. CircumcenterExplanation
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.Rate this question:
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- 13.
What is the term for the point of concurrency of the angle bisectors of a triangle?
- A.
Circumcenter
- B.
Centroid
- C.
Incenter
- D.
Orthocenter
Correct Answer
C. IncenterExplanation
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.Rate this question:
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- 14.
What is the term for the point of concurrency of the medians?
- A.
Circumcenter
- B.
Point of concurrency
- C.
Orthocenter
- D.
Centroid
Correct Answer
D. CentroidExplanation
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.Rate this question:
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- 15.
An orthocenter is the point of concurrency of the lines containing the ______.
Correct Answer
altitudesExplanation
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.Rate this question:
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Mar 20, 2023Quiz Edited by
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Nov 30, 2011Quiz Created by
Carmendianne97
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