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Geometry Chapter 3 Vocabulary
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Terms in this set (43)
alternate exterior angles
Two nonadjacent exterior angles that lie on opposite sides of a transversal.
alternate interior angles
Two nonadjacent interior angles that lie on opposite sides of a transversal.
axis of symmetry
A line that divides a planar figureinto two congruent reflected halves.
center of a regular polygon
The point that is equidistant from all vertices of a polygon.
central angle of a regular polygon
An angle formed by two rays originating from the center of a circle.
concave polygon
A polygon that is not convex.
convex polygon
A polygon in which any line segment connecting two points of the polygon has no part outside the polygon.
corresponding angles
Two nonadjacent angles, one interior and one exterior, that lie on the same side of a transversal.
equiangular polygon
A polygon in which all angles are congruent.
equilateral polygon
A polygon in which all sides are congruent.
midsegment of a trapezoid
A line connecting the midpoints of the two nonparallel segments of a trapezoid.
midsegment of a triangle
A segment whose endpoints are the midpoints of two sides.
polygon
A closed plane figure formed from three or more segments such that each segment intersects exactly two other segments, one at each endpoint and no two segments with a common endpoint are collinear.
parallelogram
A quadrilateral with two pairs of parallel sides.
quadrilateral
A polygon with four sides
rectangle
A quadrilateral with four right angles.
reflectional symmetry
A plane figure has reflectional symmetry if its reflection image across a line coincides with the preimage, the original figure.
regular polygon
A polygon that is both equilateral and equiangular.
remote interior angle
An interior angle of a triangle that is not adjacent to a given exterior angles.
rhombus
A quadrilateral with four congruent sides.
rotational symmetry
A figure has rotational symmetry if and only if it has at least one rotation image, not counting rotation images of 0˚ or multiples of 360˚, that coincides with the original figure.
same-side interior angles
Interior angles that lie on the same-side of a transversal.
slope
The ratio of rise to run for a segment; the slope of a nonvertical line that contains the points (x1, y1) is the ratio (y2-y1/x2-x1)
square
A quadrilateral with four congruent sides and four right angles.
transversal
A line, ray, or segment that intersects two or more coplanar lines, rays, or segments, each at a different point.
trapezoid
A quadrilateral with one and only one pair of parallel sides.
Corresponding Angles Postulate
If two lines cut by a transversal are parallel, then corresponding angles are congruent.
Alternate Interior Angles Theorem
If two lines cut by a transversal are parallel, then alternate interior angles are congruent.
Alternate Exterior Angles Theorem
If two lines cut by a transversal are parallel, then same-side interior angles are supplementary.
Theorem:Converse of the Corresponding Angles Postulate
If two lines are cut by a transversal in such a way that corresponding angles are congruent, then the two lines are parallel.
Converse of the Same-Side Interior Angles Theorem
If two lines are cut by a transversal in such a way that same-side interior angles are supplementary, then two lines are parallel.
Converse of the Alternate Interior Angles Theorem
If two lines are cut by a transversal in such a way that alternate interior angles are congruent, then the two lines are parallel.
Theorem
If two coplanar lines are perpendicular to the same line, then two lines are parallel.
Theorem
If two lines are parallel to the same line, then the two lines are parallel.
The Parallel Postulate
Given a line and a point not on the line, there is one and only on line that contains the given point and is parallel to the given line.
Triangle Sum Theorem
The sum of the measures of the angles of a triangle is 180˚.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Sum of the Interior Angles of a Polygon
The sum,s, of the measures of the interior angles of a polygon with n sides is given by s = (n-2)180˚.
The Measure of an Interior Angle of a Regular Polygon
The measure, m, of an interior angle of a regular polygon with n sides is m=180˚-360/n.
Sum of the Exterior Angles of a Polygon
The sum of the measures of the exterior angles of a polygon is 360˚.
Parallel Lines Theorem
In a coordinate plane, two nonvertical lines are parllel if and only if they have the same slope.
Perpendicular Lines Theorem
In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1.
Converse of the Alternate Exterior Angles Theorem
If 2 lines are cut by a transversal in such a way that alternate exterior angles are congruent.
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