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| are points all in one line |
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| is a figure formed by two rays that have the same endpoint |
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| are angles that have equal measures |
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| are two angles in a plane that a commen vertex and a common side but no common interior points |
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| is a ray that divides the angle into two congruent adjacent angles |
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| are two angles whose measures have the sum of 90. |
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| are two angles whose measures have the sum of 180 |
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| are two angles whose sides form to pairs of opposite rays |
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| Vertical angles are congruent |
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| are two lines that form two right angles |
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| Adjacent angles formed by perpendicular lines are congruent |
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| If two lines form congruent adjacent angles, then the lines are perpendicular |
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| If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary. |
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| If two angles are supplements of congruent angles ( or the same angles ), then the two angles are congruent. |
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| If two angles are complemnts of congruent angles ( or the same angle), then the two angles are congruent. |
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| A line contains at least two points; a plane contains at least three points not all in one line; a space contains at least four points not all in one plane |
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| Through any two points there is exactly one line |
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| Through any three points there is at least one plane, and through any three non collinear points there is eaxtly one plane |
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| If two points are in a plane, then the line that contains the points is in that plane |
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| if two planes intersect, then their intersection is a line |
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| if two lines intersect, then they intersect exactly at one point |
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| If there is a line and a point not in the line, then exactly one plane contains them |
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| If two lines intersect, then exactly one plane contains them. |
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| do not intersect and are coplaner |
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| do not intersect and are not coplaner |
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| if two parallel planes are cut by a third plane, then the lines of intersection are parallel |
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| is a line that intersects two or more coplaner lines in different points |
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| Alternate interior angles |
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| are two interior angles on the same side of the transversal |
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| are two interior angles on the same side of the transversal |
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| are two angles in corresponding positions relate to the two lines. |
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| If two parallel lines are cut by a transversal, then corresponding angles are congruent |
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| if two parallel lines are cut by a transversal, then alternate interior angles are congruent |
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| if two parallel lines are cut by a transversal, then same side interior angles are supplementary |
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| if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also |
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| if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel |
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| if two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel |
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| if two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel |
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| in a plane, two lines perpendicular to the same line are parallel |
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| through a point outside a line, there is exactly one line parallel to the given line |
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| through a point outside a line, there is exactly one line perpendicular to the given line |
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| Two lines parallel to a third line are parallel to each other |
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| the figure formed by three segments joining three non-collinear points |
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| at least two sides congruent |
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| is a line(ray or segment) added to a diagram to help in a proof |
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| the sum of the measures of the angle of a triangle is 180 |
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| If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent |
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| Each angle of an equiangular triangle has measure 60 |
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| in a triangle, there can be at most one right angle or obtuse angle |
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| the acute angles of a right triangle are complementary |
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| the measure of an exterior angle of a triangle equals the sum of the measure of the two remote interior angles |
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| all diagonals lie within the figure |
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| the sum of the measures of the angles of a convex polygon with n sides is (n-2)180 |
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| The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360 |
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| if a polygon is both equiangular and equilateral |
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| whenever two figures have the same size and shape |
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| if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent |
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| if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent |
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| if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent |
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| Isosceles triangle theorem |
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Definition
| if two sides of a triangle are congruent, then the angles opposite those sides are congruent |
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| an equilateral triangle is also equiangular |
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| An equilateral triangle has three 60○ angles |
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| the bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint |
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| if two angles of a triangle are congruent, then the sides opposite those angles are congruent |
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| an equiangular triangle is also equilateral |
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| if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent |
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Definition
| if the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent |
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| is a segment from a vertex to its midpoint of the opposite side |
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| is the perpendicular segment from a vertex to the line that contains the opposite side |
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| If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment |
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| if a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment |
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| if a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle |
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| if a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle |
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| a quadrilateral with both pairs of opposite sides parallel |
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| Opposite sides of a parallelogram are congruent |
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| If two lines are parallel, then all points on one line are equidistant from the other line |
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| Opposite angles of a parallelogram are congruent |
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| The diagonals of a parallelogram bisect each other |
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| If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram |
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Definition
| if one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram |
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Definition
| if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram |
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| if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram |
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| if three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal |
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| a line that contains the midpoint of one side of a triangle and is parallel to another side bisects the third side |
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| quadrilateral with four right angles |
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| quadrilateral with four congruent sides |
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| quadrilateral with four right angles and four congruent sides |
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| the diagonals of a rectangle are congruent |
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| the diagonals of a rhombus are perpendicular |
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| Each diagonal of a rhombus bisects two angles of the rhombus |
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| The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices |
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| if an angle of a parallelogram is a right angle, then the parallelogram is a rectangle |
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| if two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus |
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| a trapezoid with congruent legs |
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| Base angles of an isoceles trapezoid are congruent |
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| of a trapezoid is the segment that joins the midpoints of the legs |
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Definition
the median of a trapezoid
1. is parallel to the bases;
2. has a length equal to half the sum of the lengths of the bases |
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Definition
the segment that joins the midpoints of two sides of a triangle
1. is parallel to the third side
2. has a length equal to half the length of the third side |
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Definition
| if one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side |
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Definition
| if one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle |
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| the perpendicular segment from a point to a line is the shortest segment from the point to the line |
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| the perpendicular segment from a point to a plane is the shortest segment from the point to the plane |
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| The sum of the lengths of any two sides of a triangle is greater than the length og the third side |
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Definition
| if two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle |
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Term
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Definition
| if two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second |
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