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Show that of all line segments drawn from a given point not on it the perpendicular line segment is the shortest?
To show that the perpendicular line segment is the shortest among all line segments drawn from a given point not on it, we can use the Pythagorean theorem. Let the given point be P and the line segment be AB, with the perpendicular from P meeting AB at C. By the Pythagorean theorem, the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. In this case, PC is the hypotenuse, and AP and AC are the other two sides. Thus, AC (perpendicular line segment) will always be shorter than any other line segment AB drawn from point P.
What else can I help you with?
Which geometric shape could not be drawn using both perpendicular line segments and parallel line segments?
A circle.
How many line segments can be drawn from two points?
There is only one line (or line segment) that can be drawn between two distince points.
How many lines can be drawn that are perpendicular to a given line?
Infinity
What is an apothem?
The line drawn from the center of a regular polygon and perpendicular to a side.
A line segment drawn between two points on a circle?
Chord.
The distance from a point C to the line AB is the length of the segment from C to AB?
That is correct. The distance from a point C to a line AB is the length of the perpendicular segment drawn from point C to line AB. This forms a right angle, creating a right triangle with the segment as the hypotenuse. The length of this perpendicular segment is the shortest distance from the point to the line.
Which geometric shape could not be drawn using both perpendicular line segments and parallel line segments?
A circle.
What are four segments are perpendicular to plane ABFE?
To determine the four segments that are perpendicular to plane ABFE, we need to identify lines or segments that intersect the plane at a right angle. Typically, these segments would extend vertically from points on the plane ABFE. For example, if points A, B, F, and E define the corners of the plane, then segments from points A, B, F, and E going straight up or down would be perpendicular to the plane. Additionally, any segment drawn from a point not on the plane directly towards the plane at a right angle would also be considered perpendicular.
A line segment drawn from the center of a regular polygon perpendicular to a side of the polygon?
apothem
In a regular polygon what is the name of the segment drawn from the center of the polygon to a side that is perpendicular to that side?
Apothem!
What of a triangle is a segment drawn through the midpoint of a side forming a right angle?
It is the perpendicular bisector
How many line segments can be drawn from two points?
There is only one line (or line segment) that can be drawn between two distince points.
What is one difference between an altitude and a median of a triangle?
An altitude is a perpendicular drawn from a point to the opposite segment while a median is a segment drawn from a point to the opposite side such that it bisects the side.Altitudes and their concurrenceMedians and their concurrence
What is a space found inside a closed polygon?
A perpendicular segment drawn from a vertex to the line that contains the opposite side
Begin with a segment and a point not on the segment. fold the paper through the point so that the given line segments lies upon itself?
To achieve this, first, identify the segment and the point not on the segment. Then, fold the paper such that the segment aligns perfectly with its reflection across the folding line that passes through the point. This line should bisect the angle formed by the segment and the perpendicular drawn from the point to the segment, ensuring that the segment overlaps itself when folded. After folding, the segment and its reflection will coincide, demonstrating the desired alignment.
How many lines in a plane could be perpendicular bisectors of a segment?
In a plane, there are infinitely many lines that can serve as perpendicular bisectors of a given segment. The unique perpendicular bisector of a segment is a specific line that divides the segment into two equal parts at a right angle. However, any line parallel to this unique bisector, at any distance, can also be considered a perpendicular bisector if it intersects the segment at its midpoint. Thus, while the unique perpendicular bisector exists, an infinite number of lines can be drawn parallel to it.
If 20 points are placed on a circle and every pair of points are joined with a line segment what is the total number of segments drawn?
twenty
