Podcast
Questions and Answers
What does it mean for points to be collinear?
What does it mean for points to be collinear?
- They are all on the same line. (correct)
- They are all endpoints of line segments.
- They are all distinct points in a plane.
- They form an angle.
What are concurrent lines?
What are concurrent lines?
Three or more lines that contain the same point.
If B is between A and C, then points A, B, C are distinct ___ points.
If B is between A and C, then points A, B, C are distinct ___ points.
collinear
What can be said about points B and C in relation to point A if they are on the same side?
What can be said about points B and C in relation to point A if they are on the same side?
Define a line segment.
Define a line segment.
What is a ray?
What is a ray?
What are opposite rays?
What are opposite rays?
What constitutes an angle?
What constitutes an angle?
When does a point lie in the interior of an angle?
When does a point lie in the interior of an angle?
What are congruent line segments?
What are congruent line segments?
Define congruent angles.
Define congruent angles.
What is the midpoint of a line segment?
What is the midpoint of a line segment?
What is a line segment bisector?
What is a line segment bisector?
What is a right angle?
What is a right angle?
What is an acute angle?
What is an acute angle?
What is an obtuse angle?
What is an obtuse angle?
What are complementary angles?
What are complementary angles?
What are supplementary angles?
What are supplementary angles?
When do two lines intersect?
When do two lines intersect?
What are perpendicular lines?
What are perpendicular lines?
Define an angle bisector.
Define an angle bisector.
What is a reversed midpoint?
What is a reversed midpoint?
What defines a reversed line segment bisector?
What defines a reversed line segment bisector?
What does a reversed right angle measure?
What does a reversed right angle measure?
What is a reversed angle bisector?
What is a reversed angle bisector?
What defines a reversed congruent angle?
What defines a reversed congruent angle?
What are reversed congruent line segments?
What are reversed congruent line segments?
Define adjacent angles.
Define adjacent angles.
What is a linear pair?
What is a linear pair?
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Study Notes
Collinear and Concurrent
- Collinear points are three or more points lying on the same line.
- Concurrent lines are three or more lines that intersect at a single point.
Geometric Relations
- Point B is between points A and C if A, B, and C are distinct collinear points with AB + BC = AC.
- Points B and C are on the same side of point A if A, B, and C are collinear and A does not lie between B and C.
Line and Its Components
- A line segment consists of two endpoints and all points in between.
- A ray has a fixed starting point and extends infinitely in one direction.
- Opposite rays share a common endpoint and extend in opposite directions.
Angles
- An angle is formed by two rays that meet at a common endpoint known as the vertex.
- A point lies in the interior of an angle if two points exist on each ray, and the interior point lies between them.
Congruence
- Congruent line segments are those of equal length.
- Congruent angles measure the same, indicating equality in angle size.
Midpoints and Bisectors
- The midpoint of a line segment is the point dividing it into two congruent segments.
- A line segment bisector intersects a segment at its midpoint.
Angle Types
- A right angle measures exactly 90 degrees.
- Acute angles measure less than 90 degrees and more than 0 degrees.
- Obtuse angles are greater than 90 degrees but less than 180 degrees.
Angle Relationships
- Complementary angles' measures sum to 90 degrees.
- Supplementary angles' measures add up to 180 degrees.
Intersections and Perpendicularity
- Lines intersect if they share at least one point.
- Perpendicular lines intersect at a right angle (90 degrees).
Angle and Line Segment Properties
- An angle bisector divides an angle into two congruent angles and originates from the angle's vertex.
- A reversed midpoint and segment bisector principles affirm congruence in segments created through division.
Angular Relationships and Properties
- Adjacent angles share a vertex and a side but do not overlap.
- Linear pairs consist of two adjacent angles whose non-shared sides are opposite rays, forming a straight line together.
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