Term
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Definition
| Collinear points are points that lie on the same line. |
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Definition
| Noncollinear points are points that do not lie on the same line. |
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Term
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Definition
| A line segment is a part of a line consisting of two points, called end points, and the set of all points between them. |
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Term
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Definition
| Congruent line segments are line segments that have equal lengths. |
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Definition
| If F, G, and H are collinear, and if FG+GH=FH, then G is between F and H. |
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Term
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Definition
| A ray is a part of a line consisting of a given point, called the end point, and the set of all points on one side of the end point. |
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Definition
| An angle is the union of two rays having the same end point. The end point is called the vertex of the angle; the rays are called the sides of the angle. |
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Definition
| Congruent angles are angles that have equal measures. |
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Definition
| Betweenness of rays: PS is between PQ and PR, if point S lies in the interior of |
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Term
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Definition
| A right angle is an angle with a measure of 90 degrees. |
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Term
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Definition
| An acute angle is an angle with a measure of less than 90 degrees. |
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Term
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Definition
| An obtuse angle is an angle with a measure great the 90, but less than 180 degrees. |
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Term
| Midpoint of a Line Segment |
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Definition
| The midpoint of a line segment is the point that divides the line segment into two congruent line segments. |
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Term
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Definition
| A bisector of AB is any line, ray, or line segment which passes throught the midpoint of AB. |
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Term
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Definition
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Term
| Postulate 1 (two point determine) |
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Definition
| Two points determine a unique straight line. |
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Term
| Postulate 2(three noncollinear points determine) |
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Definition
| Three noncollinear points determine a unique plane. |
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Term
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Definition
| a) To every point on a line, there corresponds exactly one real number called its coordinate. b)To every real number, there corresponds exactly one point of the line. c) To every pair of points there corresponds exactly one real number called the distance between points. d) And the distance between the points is the absolute calue of the difference between their coordinates. |
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Term
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Definition
| a) The rays in a half rotation (180 degrees) can be numbered so that to every ray there corresponds exactly one real number called its coordinate. b) And to every real number from 0 to 180, there corresponds exactly one ray. c) To every pair of rays there corresponds exactly one real number called the measure of the angle that they determine. d) and the measure of the angle is the absolute value of the difference between the coordinates of its rays. |
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Term
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Definition
| If equals are added to equals the results are equal: If a=b then a+c=b+c |
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Term
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Definition
| If equals are subtracted from equals, the results are equal: If a=b, then a-c+b-c |
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Term
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Definition
| If equals are multiplied by equals, their products are equal: If a=b, then ac=bc |
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Definition
| If equals are divided by nonzero equals, their quotients are equal: If a=b, then a/c=b/c as long as c doesn't =0 |
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Term
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Definition
| If a=b, then either a or b may be substituted for the other in any equation. |
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Term
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Definition
| If two quantities are eqaul to the same quantity, then they are equal to each other: If a=b and b=c, then a=c. |
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Term
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Definition
| Any quantity is equal to itself: a=a. |
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Term
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Definition
| The positions of the expressions on either side of an equals sign may be reversed. If a=b, then b=a. |
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Term
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Definition
| Complementary angles are angles with measures that add to 90 degrees. |
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Term
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Definition
| Supplementary angles are angles with measures that add to 180 degrees. |
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Term
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Definition
| Adjacent angles are angles that have the same vertex, share a common side, and have no interior points in common. |
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Term
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Definition
| A linear pair is two adjacent angles whose exterior sides form a straight line. |
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Term
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Definition
| Vertical angles are a pair of nonadjacent angles formed by two intersecting lines. |
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Term
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Definition
| Perpendicular lines are lines which intersect to form right angles. |
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Term
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Definition
| A perpendicular bisector is a line that is perpendicular to a line segment and intersects the line segment at its midpoint. |
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Term
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Definition
| The distance between two points is the length of the lines segment joining the points. |
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Term
| Distance Between a Line and a Point not on the Line |
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Definition
| The distance between a line and a point not on the line is the length of the perpendicular segment drawn from the point to the line. |
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Term
| Theorem 1 (two angles complimentary to the same angle) |
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Definition
| If two angles are complementary to the same angle or congruent angles, then they are congruent. |
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Term
| Theorem 2 (two angles supplementary to the same angle) |
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Definition
| If two angles are supplementary to the same angle or congruent angles, then they are congruent. |
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Term
| Theorem 3 (two angles are a linear pair) |
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Definition
| If two angles are a linear pair, then they are supplementary. |
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Term
| Theorem 4 (pairs of vertical angles) |
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Definition
| Pairs of vertical angles are congruent. |
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Term
| Theorem 5 (perpendicular lines intersect to form) |
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Definition
| Perpendicular lines intersect to form 4 right angles. |
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Term
| Theorem 6 (right angles are) |
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Definition
| All right angles are congruent. |
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Term
| Theorem 7 (given point on a lines, exactly one perpendicular point) |
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Definition
| Through a given point on a line, there exists exactly one perpendicular to the given line. |
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Term
| Theorem 8 (exterior sides of a pair of adjacent angles are perpendicular) |
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Definition
| If the exterior sides of a pair of adjacent angles are perpendicular, the angles are complimentary. |
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Term
| Postulate 5 (given point not on a line, exists exactly one perpendicular point) |
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Definition
| Through a given point Not on a line, there exists exactly one perpendicular to the given line. |
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Term
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Definition
| Parallel lines are lines that lie in the same plane (coplanar) and that never intersect. |
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Term
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Definition
| Lines, segments, rays and points which lie in the same plane are said to be coplanar. |
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Term
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Definition
| A transversal is a line that intersects two or more lines in different points. |
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Term
| Theorem 9 (parallel lines crossed by a transversal) |
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Definition
| If two parallel lines are cut by a transveral, then their corresponding andles are congruent. |
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Term
| Theorem 10 (two angles of a linear pair are congruent) |
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Definition
| If the two angles in a linear pair have equal measures, then each is a right angle. |
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Term
| Theorem 11 (two parallel lines cut by a transversal, alternate exterior angles) |
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Definition
| If two parallel lines are cut by a transversal, then their alternate exterior angles are congruent. |
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Term
| Theorem 12 (two parallel lines cut by a transversal, interior angles on the same side of the transversal) |
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Definition
| If two parallel lines are cut by a transversal, then their interior angles on the same side of the transversal are supplementary) |
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Term
| Theorem 13 (congruent corresponding angles with a transversal) |
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Definition
| If two lines form congruent corresponding angles with a transversal, then the lines are parallel. |
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Term
| Theorem 14 (congruent alternate exterior angles with a transversal) |
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Definition
| If two lines form congruent alternate exterior angles with a transversal, then the lines are parallel. |
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Term
| Theorem 15 (supplementary interior angles on the same side of a transversal) |
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Definition
| If two lines form supplementary interior angles on the same side of a transversal, then the lines are parallel. |
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Term
| Postulate 6 (two parallel lines cut by a transversal, alternate interor angles) |
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Definition
| If two parallel lines are cut by a transversal, then their alternate interior angles are congruent. |
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Term
| Postulate 7 (two lines form congruent alternate interior angles with a transversal) |
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Definition
| If two lines form congruent alternate interior angles with a transversal, then the lines are parallel. |
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Term
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Definition
| A polygon is a geometric figure whose sides are line segments. |
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Term
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Definition
| A triangle is a polygon that has three sides. |
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Term
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Definition
| A scalene triangle has no congruent sides. |
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Term
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Definition
| An isosceles triangle has two congruent sides. |
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Term
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Definition
| An equilateral triangle has all three congruent sides. |
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Term
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Definition
| An acute triangle has all three angles with measures of less than 90 degrees. |
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Term
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Definition
| A right triangle has one angle with a measure of 90 degrees. |
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Term
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Definition
| An obtuse triangle has one angle with a measure greater than 90 degrees. |
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Term
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Definition
| An equiangular triangle has all three angles with equal measures. |
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Term
| Exterior Angle of a Polygon |
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Definition
| An exterior angle of a polygon is an angle that forms a linear pair with one of the interior angles of the polygon. |
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Term
| Definition of Congruent Triangles |
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Definition
| If the vertices of two triangles can be paired in a correspondence so that all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent, then the triangles are congruent. |
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Term
| Theorem 16 (two lines parallel to a third line) |
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Definition
| If two lines are parallel to a third line, then the lines are parallel to each other. |
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Term
| Theorem 17 (sum of the measures of the angles of a triangle) |
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Definition
| The sum of the measures of the angles of a triangle is 180. |
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Term
| Corollary 17.1 (acute angle of right triangles) |
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Definition
| The acute angles of a right triangle are complementary. |
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Term
| Corollary 17.2 (measure of the angles of an equiangular triangle) |
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Definition
| The measure of each angle of an equiangular triangle is 60. |
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Term
| Corollary 17.3 (two angles of a triangle are congruent to two angles of another triangle) |
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Definition
| If two angles of a triangle are congruent to two angles of another triangle, then the remaining pair of angles are congruent. |
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Term
| Exterior Angle of a Triangle Theorem |
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Definition
| The measure of an exterior angle of a triangle is equal to the sum of the measure of the two remote interior angles. |
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Term
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Definition
| If the vertices of two triangles can be paired so that two angles and the side opposite one of them in one triangle are congruent to the corresponding parts of the second triangle, then the two triangles are congruent. |
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Term
| Postulate 8 (given point not on a line, one parallel line may be drawn) |
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Definition
| Through a given point not on a line, exactly one line may be drawn parallel to the line. |
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Term
| Side-Angle-Side Postulate |
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Definition
| If the vertices of two triangles can be paired so that two sides and the included angle of one triangle are congruent to the corresponding parts of the second triangle, then the two triangles are congruent. |
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Term
| Angle-Side-Angle Postulate |
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Definition
| If the vertices of two triangles can be paired so that two angles and the included side of one triangle are congruent to the corresponding parts of the second triangle, then the two triangles are congruent. |
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Term
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Definition
| If the vertices of two right triangles can be paired so that the hypotenuse and leg of one of them are congruent to the corresponding parts of the second right triangle, then the two right triangles are congruent. |
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Term
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Definition
| If the vertices of two triangles can be paired so that three sides of one triangle are congruent to the corresponding sides of the second triangle, then the two triangles are congruent. |
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Term
| Corresponding Parts of Congruent Triangles are Congruent (CPCTC) |
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Definition
| If two triangles are congruent, then their vertices can be paired in a correspondence so that all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent. |
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Term
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Definition
| An altitude of a triangle is a segment drawn from any vertex of the triangle, perpendicular to the opposite side, extended outside the triangle if necessary. |
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Term
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Definition
| A median of a triangle is a segment drawn from any vertex of the triangle to the midpoint of the opposite side. |
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Term
| Theorem 20 (two triangles congruent to the same triangle) |
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Definition
| If two triangles are congruent to the same triangle, then they are congruent to each other. |
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Term
| Theorem 21 (point that lies on the perpendicular bisector of a segment) |
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Definition
| 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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Term
| Theorem 22 (a point that is equidistant from the endpoints of a segment) |
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Definition
| 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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Term
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Definition
| If twp sodes of a triangle are congruent, then the angles opposite those sides are congruent. |
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Term
| Corallary 23.1 (equilateral triangle) |
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Definition
| If a triangle is equilateral, then it is also equiangular. |
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Term
| Theorem 24 (altitudes extending to the legs of an isosceles triangle) |
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Definition
| The altitudes extending to the legs of an isosceles triangle are congruent. |
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Term
| Theorem 25 (two angles of a triangle are congruent) |
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Definition
| If two angles of a triangle are congruent, then the sides opposite those angles are congruent. |
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Term
| Corollary 25.1 (equiangular triangle) |
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Definition
| If a triangle is equiangular, then it is also equilateral. |
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Term
| Theorem 26 (medians extending to the legs of isosceles triangles) |
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Definition
| The medians extending to the legs of an isosceles triagle are congruent. |
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