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98 Cards in this Set
- Front
- Back
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Chapter 1
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Discovering Points, Lines, Planes, and Angles
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Ruler Postulate
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The points on any line can be paired with the real numbers so that, given any two points P and Q on the line, P corresponds to zero, and Q corresponds to a positive number.
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Segment Addition Postulate
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If Q is between P and R,
then (PQ +QR = P). If PQ + QR = PR, then Q is between P and R. |
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Protractor Postulate
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Given ray AB and a number r between 0 and 180,
there is exactly one ray with endpoint A, extending on each size of ray AB, such that the measure of the angle formed is r. |
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Angle Addition Postulate
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If R is in the interior of <PQS,
then (m<PQR + m<RQS = m<PQS). If (m<PQR + m<RQS = m<PQS), then R is in the interior of <PQS. |
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Midpoint Theorem
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If M is the midpoint of line AB,
then (line AM) is congruent to (line MB). |
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Chapter 2
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Connecting Reasoning and Proof
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Through any two points there is exactly one _____.
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Through any two points there is exactly one line.
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Through any three noncollinear points, there is exactly one _____.
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Through any three noncollinear points, there is exactly one plane.
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A line contains at least two _____.
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A line contains at least two points.
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If two points lie in a plane, then the entire _____ containing those two points lies in that plane.
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If two points lie in a plane, then the entire line containing those two points lies in that plane.
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A plane contains at least three _____ not on the same line.
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A plane contains at least three points not on the same line.
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If two planes intersect, then their intersection is a _____.
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If two planes intersect, then their intersection is a line.
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Congruence of segments is _____, _____, and _____.
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Congruence of segments is reflexive, symmetric, and transitive.
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Supplement Theorem
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If two angles form a linear pair, then they are supplementary angles.
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Angles supplementary to the same angle or to congruent angles are _____.
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Angles supplementary to the same angle or to congruent angles are congruent.
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Congruence of angles is _____, _____, and _____.
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Congruence of angles is reflexive, symmetric, and transitive.
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Angles complementary to the same angle or to congruent angles are _____.
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Angles complementary to the same angle or to congruent angles are congruent.
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All right angles are _____.
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All right angles are congruent.
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Vertical angles are _____.
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Vertical angles are congruent.
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Perpendicular lines intersect to form four _____ angles.
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Perpendicular lines intersect to form four right angles.
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Chapter 3
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Using Perpendicular and Parallel
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Corresponding Angles Postulate
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If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
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Alternate Interior Angles Theorem
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If two parallel lines are cut by a traversal, then each pair of alternate interior angles is congruent.
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Consecutive Interior Angles Theorem
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If two parallel liens are cut by a transversal, then each pair of consecutive interior angles is supplementary.
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Alternate Exterior Angles Theorem
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If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.
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Perpendicular Transversal Theorem
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In a plane, if a line is perpendicular to one of two parallel lines,m then it is perpendicular to the other.
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Two non-vertical lines have the same slope if and only if they are _____.
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Two non-vertical lines have the same slope if and only if they are parallel.
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Two non-vertical lines are perpendicular if and only if the product of their slopes is _____.
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Two non-vertical lines are perpendicular if and only if the product of their slopes is -1.
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If two lines in a plane are cut by a transversal so that the corresponding angles are congruent, then the lines are _____.
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If two lines in a plane are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel.
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Parallel Postulate
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If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.
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If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are _____.
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If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are parallel.
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If two lines in a plane are cut by a _____ so that a pair of consecutive interior angles is supplementary, then the lines are parallel.
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If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.
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If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is _____, then the lines are parallel.
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If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel.
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In a plane, if two lines are perpendicular to the same line, then they are _____.
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In a plane, if two lines are perpendicular to the same line, then they are parallel.
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Chapter 4
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Identifying Congruent Triangles
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Angle Sum Theorem
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The sum of the measure so f the angles of a triangle is 180.
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Third Angle Theorem
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If two angles of on e triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.
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Exterior Angle Theorem
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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
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The acute angles of a right triangle are _____.
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The acute angles of a right triangle are complementary.
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There can be at most one right or _____ angle in a triangle.
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There can be at most one right or obtuse angle in a triangle.
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Congruence of triangle is _____, _____, and _____.
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Congruence of triangle is reflexive, symmetric, and transitive.
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SSS Postulate
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If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
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SAS Postulate
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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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ASA Postulate
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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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AAS Theorem
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If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, the two triangles are congruent.
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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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If two angles of a triangle are congruent, then the sides opposite those angles are _____.
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If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
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A triangle is equilateral if and only if it is _____.
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A triangle is equilateral if and only if it is equiangular.
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Each angle of an equilateral triangle measures _____.
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Each angle of an equilateral triangle measures 60°.
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Chapter 5
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Applying Congruent Triangles
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A point on the perpendicular bisector of a segment is equidistant from the _____ of the segment.
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A point on the perpendicular bisector of a segment is equidistant fro the endpoints of the segment.
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A point equidistant from the endpoints of a segment lies on the perpendicular _____ of the segment.
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A point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment.
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A point on the bisector of an angle is equidistant from the sides of the _____.
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A point on the bisector of an angle is equidistant from the sides of the angle.
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A point on or in the interior of an angle and equidistant from the sides of an angle lies on the _____ of the angle.
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A point on or in the interior of an angle and equidistant from the sides of an angle lies on the bisector of the angle.
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Leg-Leg Congruence of Right Triangles Theorem
LL |
If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent.
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Hypotenuse-Angle Congruence of Right Triangles Theorem
HA |
If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent.
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Leg-Angle Congruence of Right Triangles Theorem
LA |
If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.
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Hypotenuse-Leg Congruence of Right Triangles Theorem
HL |
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.
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Exterior Angle Inequality Theorem
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If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles.
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If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.
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If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.
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If one angle of a triangle has a greater measure than another angle, then the side _____ the greater angle is longer than the side opposite the lesser angle.
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If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
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The perpendicular segment from a point to a line is the _____ segment from the point to the line.
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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 _____ segment from the point to the plane.
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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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Triangle Inequality Theorem
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The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
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SAS Inequality
(Hinge Theorem) |
If two sides of one triangle are congruent to two sides of another triangle, and the included angle in one triangle is greater than the included angle in the other, then the third side of the first triangle is longer than the third side in the second triangle.
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SSS Inequality
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If two sides of one triangle are congruent to two sides of another triangle and the third side in another triangle is longer than the third side in the other, then the angle between the pair of congruent sides in the first triangle is greater than the corresponding angle in the second triangle.
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Chapter 6
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Exploring Quadrilaterals
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Opposite sides of a parallelogram are _____.
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Opposite sides of a parallelogram are congruent.
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Opposite angles of a parallelogram are _____.
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Opposite angles of a parallelogram are congruent.
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Consecutive angles in a parallelogram are _____.
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Consecutive angles in a parallelogram are supplementary.
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The diagonals of a parallelogram _____ each other.
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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 _____.
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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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If the diagonals of a quadrilateral _____ each other, 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 one pair of opposite sides of a quadrilateral are both _____ and _____, then the quadrilateral is a parallelogram.
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If one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram.
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If a parallelogram is a rectangle, then its diagonals are _____.
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If a parallelogram is a rectangle, then its diagonals are congruent.
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If the diagonals of a parallelogram are _____, then the parallelogram is a rectangle.
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If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
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The diagonals of a rhombus are _____.
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The diagonals of a rhombus are perpendicular.
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If the diagonals of a parallelogram are perpendicular, then the parallelogram is a _____.
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If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
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Each diagonal of a rhombus _____ a pair of opposite angles.
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Each diagonal of a rhombus bisects a pair of opposite angles.
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Both pairs of base angles of an _____ trapezoid are congruent.
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Both pairs of base angles of an isosceles trapezoid are congruent.
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The diagonals of an isosceles trapezoid are _____.
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The diagonals of an isosceles trapezoid are congruent.
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The median of a trapezoid is parallel to the bases, and its measure is _____ the sum of the measures of the bases.
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The median of a trapezoid is parallel to the bases, and its measure is one-half the sum of the measures of the bases.
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Chapter 7
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Connecting Proportion and Similarity
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AA Similarity
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If two angles of one triangle are congruent o two angles of another triangle, then the triangles are similar.
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SSS Similarity
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If the measures of the corresponding sides of two triangles are proportional, then the triangles are similar.
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SAS Similarity
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If the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.
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Similarity of triangles is _____, _____, and _____.
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Similarity of triangles is reflexive, symmetric, and transitive.
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Triangle Proportionality
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If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional lengths.
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If a line intersects two sides of a triangle and separates the sides into _____ segments of proportional lengths, then the line is parallel to the third side.
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If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side.
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A segment whose endpoints are the midpoints of two sides of a triangle is parallel to the third side of the triangle and its length is _____ the length of the third side.
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A segment whose endpoints are the midpoints of two sides of a triangle is parallel to the third side of the triangle and its length is one half the length of the third side.
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If three or more parallel lines intersect two transversals, then they cut off the transversal _____.
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If three or more parallel lines intersect two transversals, then they cut off the transversal proportionally.
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If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on _____ transversal.
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If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
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Proportional Perimeters
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If two triangles are similar, then the perimeters are proportional to the measures of corresponding sides.
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If two triangles are _____, then the measures of the corresponding altitudes are proportional to the measures of the corresponding sides.
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If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures of the corresponding sides.
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If two triangles are similar, then the measures of the corresponding angle bisectors are proportional to the measures of the _____ sides.
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If two triangles are similar, then the measures of the corresponding angle bisectors are proportional to the measures of the corresponding sides.
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If two triangles are _____, then the measures of the corresponding medians are proportional to the measures of the corresponding sides.
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If two triangles are similar, then the measures of the corresponding medians are proportional to the measures of the corresponding sides.
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Angle Bisector Theorem
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An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides.
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