Second Quarter Test – Flashcards
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equidistant
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the distance between tow lines measured along a perpendicular line is always the same
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parallel lines
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coplanar lines that do no intersect
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parallel planes
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planes that do not intersect
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point-slope form
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an equation of the form y-y1=m(x-x1), where (x1,y1) are the coordinated of any point on the line and m is the slope of the line
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rate of change
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describes how a quantity is changing over time
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slope
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for a (nonvertical) line containing two points (x1,y1) and (x2,y2), the number m given by the formula m-y2-y1/x2-x1, where x2 is never equal to x1
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slope-intercept form
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a linear equation of the form y=mx+b; the graph of such an equation has slope m and y-intercept b
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transversal
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a line that intersects two or more lines in a plane at different points
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acute triangle
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a triangle in which all of the angles are acute angles
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base angles of an isosceles triangle
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the angles opposite the legs (congruent sides); the side opposite the vertex angle
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congruence transformations
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a mapping for which a geometric figure and its image are congruent
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coordinate proof
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a proof that uses figures in the coordinate plane and algebra to prove geometric concepts
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corollary
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a statement that can be easily proved using a theorem is this of a theorem
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equiangular triangle
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a triangle with all angles congruent
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equilateral triangle
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a triangle with all sides congruent
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exterior angle
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an angle formed by one side of a triangle and the extension of another side
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flow proof
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a proof that organizes statement in logical order in a box with the reason verifying the statement written below the box. Arrows are used to indicate the order of the statements
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included side
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the side of a triangle that is a side of each of two angles
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isosceles triangle
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a triangle with at least two sides congruent; the congruent sides are called legs; the angles opposite the legs are base angles; the angle formed by the two legs is the vertex angle; the side opposite the vertex angle is the base
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obtuse triangle
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a triangle with an obtuse base
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remote interior angles
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the angles of a triangle that are not adjacent to a given exterior angle
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right angle
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an angle with a degree measure of 90
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scalene triangle
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a triangle with no two sides congruent
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vertex of an angle
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the common endpoint of an angle; the angle formed by the two legs
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altitude
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in a triangle, a segment from a vertex of the triangle to the line containing the opposite side and perpendicular to that side; in a prism or cylinder, a segment perpendicular to the bases with an endpoint in each plane; in a pyramid or cone, the segment that has the vertex as one endpoint and is perpendicular to the base; in a paralellogram, any segment perpendicular to the bases, with endpoints on each base
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centroid
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the point of concurrency of the medians of a triangle
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circumcenter
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the point of concurrency of the perpendicular bisectors of a triangle
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concurrent lines
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three or more lines that intersect at a common point
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incenter
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the point of concurrency of the angle bisectors of a triangle
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indirect proof
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one assumes that the statement to be proved is false; one then uses logical reasoning to deduce that a statement contradicts a postulate, theorem, or one of the assumptions; once a contradiction is obtained, one concludes that the statement assumed false must in fact be true
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indirect reasoning
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reasoning that assumes that the conclusion is false and then shows that this assumption leads to a contradiction of the hypothesis or some other accepted fact, like a postulate, theorem, or corollary; then, since the assumption has been proven false, the conclusion must be true
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median
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in a triangle, a line segment with endpoints that are a vertex of a triangle and the midpoint of the side opposite the vertex; in a trapezoid, the segment that joins the midpoint of the legs
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orthocenter
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the point of concurrency of the altitudes of a triangle
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perpendicular bisector
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in a triangle, a line, segment, or ray that passes through the midpoint of a side and is perpendicular to that side
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point of concurrency
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the point of intersection of concurrent lines
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proof of contradiction
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an indirect proof in which one assumes that the statement to be proved is false; one then uses logical reasoning to deduce a statement that contradicts a postulate, theorem, or one of the assumptions; once a contradiction is obtained, one concludes that the statement assumed false must in fact be true
