Construct basic geometric figures - Common Core: High School - Geometry
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What must occur to construct two 
angles from a 
angle?
What must occur to construct two
To construct two 
angles from a 
angle a bisection must occur. Recall that bisection means to cut an angle into two equal parts.
Since
that makes a bisection of the 
angle equal two 
angles and thus is the solution.
Moving the terminal ray will not create two angles and thus it cannot be the solution.
Nonterminal is not the correct terminology and therefore, it cannot be the correct solution.
To construct two
Since
that makes a bisection of the
Moving the terminal ray will not create two angles and thus it cannot be the solution.
Nonterminal is not the correct terminology and therefore, it cannot be the correct solution.
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How are congruent lines identified in a parallelogram?
How are congruent lines identified in a parallelogram?
Parallel lines by definition are lines that will never intersect one another. This means the slope of the lines are the same. When these lines make up a parallelogram figures that are created include squares, rectangles, diamonds, and rhombi.
Some images that depict parallelograms are as follows. Notice that either single or double hash marks can be used to identify that opposite lines are congruent.
Parallel lines by definition are lines that will never intersect one another. This means the slope of the lines are the same. When these lines make up a parallelogram figures that are created include squares, rectangles, diamonds, and rhombi.
Some images that depict parallelograms are as follows. Notice that either single or double hash marks can be used to identify that opposite lines are congruent.
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Given the point 
, how would perpendicular lines be constructed?
Given the point
To construct perpendicular lines first recall what it means to be perpendicular.
Recall that perpendicular lines intersect at one point and have opposite, reciprocal slopes.
Plotting the given point is as follows:
Given this point, there are numerous combinations of perpendicular lines that can be made. Looking at the possible options the only pair that intersect at the point 
is when a vertical line is drawn at 
and a horizontal line at 
.
To construct perpendicular lines first recall what it means to be perpendicular.
Recall that perpendicular lines intersect at one point and have opposite, reciprocal slopes.
Plotting the given point is as follows:
Given this point, there are numerous combinations of perpendicular lines that can be made. Looking at the possible options the only pair that intersect at the point
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Determine whether the statement is true or false:
Lines that have fractional slopes cannot be perpendicular to other lines.
Determine whether the statement is true or false:
Lines that have fractional slopes cannot be perpendicular to other lines.
For two lines to be perpendicular they must intersect at one point and have the opposite reciprocals on each other. Having slopes that are opposite reciprocals creates a 
angle between the two lines which is also by definition makes the two lines perpendicular.
Therefore, a line that has a fractional slope can also have a perpendicular line. If the line in question has a slope of 
then the perpendicular line would have a slope of 
.
Thus, the statement, "Lines that have fractional slopes cannot be perpendicular to other lines." is false.
For two lines to be perpendicular they must intersect at one point and have the opposite reciprocals on each other. Having slopes that are opposite reciprocals creates a
Therefore, a line that has a fractional slope can also have a perpendicular line. If the line in question has a slope of
Thus, the statement, "Lines that have fractional slopes cannot be perpendicular to other lines." is false.
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Determine whether the statement is true or false:
An equilateral triangle must have sides of equal length but the interior angles may differ.
Determine whether the statement is true or false:
An equilateral triangle must have sides of equal length but the interior angles may differ.
By definition an equilateral triangle has all sides that are of equal length and angles are also equal. All interior angles on an equilateral triangle equal 
regardless of the side lengths.
Therefore, the statement "An equilateral triangle must have sides of equal length but the interior angles may differ." is false.
By definition an equilateral triangle has all sides that are of equal length and angles are also equal. All interior angles on an equilateral triangle equal
Therefore, the statement "An equilateral triangle must have sides of equal length but the interior angles may differ." is false.
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Determine whether the statement is true or false:
In a parallelogram, opposite sides are always congruent.
Determine whether the statement is true or false:
In a parallelogram, opposite sides are always congruent.
Using corresponding parts of congruent triangles proves this statement true.
A parallelogram is a four sided figure that has opposite parallel sides. Further more, when a parallelogram is divided into two triangles by drawing a line diagonally, they are equal triangles and thus the corresponding sides of each triangle are equal which in turn, makes the sides of the parallelogram congruent.
Using corresponding parts of congruent triangles proves this statement true.
A parallelogram is a four sided figure that has opposite parallel sides. Further more, when a parallelogram is divided into two triangles by drawing a line diagonally, they are equal triangles and thus the corresponding sides of each triangle are equal which in turn, makes the sides of the parallelogram congruent.
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