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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.
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
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
What is the perpendicular line segment construction?
The perpendicular line segment construction involves creating a line segment that meets another line at a right angle (90 degrees). This is typically done using a compass and straightedge. First, a point is marked on the line where the perpendicular will intersect. Then, arcs are drawn from this point to establish two points equidistant from it, allowing the straightedge to connect these points, forming a perpendicular line.
What is isotomic?
Isotomic refers to points that have equal distance from two given points. In geometry, these points lie on the perpendicular bisector of the line segment connecting the two given points.
How do you indicate congruent segments in a diagram How do you indicate congruent angles in a diagram?
Drawing two tiny parallel lines over the segment will indicate that it is a congruent segment. The little arc symbol can also be drawn over the segment or the angles.
