Geometry Midterm Study Guide – Flashcards
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converse of the alternate exterior angles theorem
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if two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel
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converse of the same-side exterior angles theorem
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if two lines and a transversal form same-side exterior angles that are supplementary, then the two lines are parallel
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equiangular
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all angles congruent
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equilateral
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all sides congruent
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isosceles
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at least two sides congruent
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scalene
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no sides congruent
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postulate
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an accepted statement or fact
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converse of isosceles triangle theorem
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if two angles of a triangle are congruent, then the sides opposite the angles ar congruent
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ray
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the part of a line consisting of one endpoint and all the points of the line on one side of the endpoint.
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isosceles triangle theorem
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if two sides of a triangle are congruent, then the angles opposite those sides are congruent
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triangle midsegment theorem
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if a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length
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skew lines
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non coplanar; therefore they are not parallel and do not intersect
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perpendicular bisector theorem
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if a point is on the perpendicular bisector of a segment then it is equidistant from the endpoints of the segment
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vertical angles
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two angles whose sides are opposite rays
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adjacent angles
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two coplanar angles with a common side, a common vertex, and no common interior points
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complementary angles
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two angles whose measure add up to 90 degrees
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supplementary angles
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two angles whose sums add up to 180
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perpendicular lines
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two lines that intersect to form right angles
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perpendicular bisector
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of a segment, is a line, segment, or ray that is perpendicular to the segment at its midpoint; forms two congruent segments
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angle bisector
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a ray that divides an angle into two congruent coplanar angles.
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vertical angles theorem
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vertical angles are congruent
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congruent supplements theorem
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if two angles are supplements of the same angle then two angles are congruent
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congruent compliments theorem
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if two angles are compliments (complimentary) of the same angle then the two angles are congruent
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transversal
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a line that intersects two coplanar lines at two distinct endpoints
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corresponding angles postulate
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if a transversal intersects two parallel lines, then corresponding angles are congruent
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alternate interior angles theorem
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if a transversal intersects two parallel lines, then the alternate interior angles are congruent
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same-side interior angles theorem
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if a transversal intersects two parallel lines, the the same-side interior angles are supplementary
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alternate exterior angles theorem
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if a transversal intersects two parallel lines, then alternate exterior angles are congruent
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same-side exterior theorem
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if a transversal intersects two parallel lines, then the same-side exterior angles are supplementary
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converse of the corresponding angles postulate
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if two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.
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converse of the alternate interior angles theorem
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if two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel
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converse of the same-side interior angles theorem
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if two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel
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converse of the perpendicular bisector theorem
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if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
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angle bisector theorem
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if a point is on the bisector of an angle then the point is equidistant from the sides of an angle
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converse of the angle bisector theorem
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if a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector
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corollary to the triangle exterior angles theorem
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the measure of an exterior angle of a triangle is greater then the measure of each of its remote interior angles
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3 - sides
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triangle
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4 -sides
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quadrilateral
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5- sides
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pentagon
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6-sides
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hexagon
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8-sides
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octagon
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9-sides
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nonagon
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10 sides
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decagon
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12 sides
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dodecagon
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n sides (13 and up)
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n-gon
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altitude of a triangle
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the perpendicular segment from a vertex to the line containing the opposite side
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circumcenter of a triangle
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the point of concurrency of the perpendicular bisectors of a triangle
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centroid
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the point of concurrency of the medians
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orthocenter of the triangle
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in a triangle the point of concurrency of the altitudes
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incenter of a triangle
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the point of concurrency of the angle bisectors in a triangle
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median of a triangle
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a segment whose endpoints are a vertex and the midpoint of the opposite side
