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39 Cards in this Set
- Front
- Back
- 3rd side (hint)
Segment Addition Postulate
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If Q is between P and R, then PQ + QR = PR
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Angle Addition Postulate
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If R is in the interior of <PQS, then m<PQS = m<PQR + m<RQS
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Reflexive Property
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For any number a, a=a
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17 = 17
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Symmetric Property
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for any numbers a and b, if a=b, then b=a
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17 = 1D
∴ 1D = 17 |
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Transitive Property
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for any numbers a, b, and c, if a=b and b=c, then a=c.
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1D = 17
5B = 1D ∴ 5B = 17 |
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Addition Property of Equality
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if a=b, then a+c=b+a
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1D = 17
1D + 3 = 17 + 3 (20) |
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Subtraction Property of Equality
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if a=b, then a-c = b-c
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1D = 17
1D - 3 = 17 - 3 (14) |
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Multiplication Property of Equality
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if a=b, then a*c=b*c
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1D = 17
1D * 3 = 17 * 3 (51) |
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Division Property of Equality
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if a = b, then a/c = b/c
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1D = 17
1D/3 = 17/3 (5.667) |
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Substitution Property
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if a = b, then b can be substituted for a.
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D = O
1D = 17 1O = 17 |
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Definition of...
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Use definitions when you are restating the same information in a new form.
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M = midpoint of AB
∴ AM = MB (definition of midpoint) |
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Linear Pair Postulate
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If two angles form a linear pair, then they are supplementary angles.
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∴ m<1 + m<2 = 180
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Congruent Supplements Theorem
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Angles supplementary to the same angle are congruent.
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∴ m<1 = m< 3
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Congruent Complements Theorem
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Angles complementary to the same angle are congruent.
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Vertical Angles Theorem
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Vertical angles are congruent.
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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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∴ m<1 = m<2
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Alternate Interior Angles Theorem
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If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
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(The angles that are 64 degrees are INTERIOR to lines KO and LN)
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Same Side (Consecutive) Interior Angles Theorem
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If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
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∴ <3 = <5
∴ <6 = <4 |
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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 consecutive interior angles is supplementary.
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Converse of Corresponding Angles Postulate
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If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.
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∴ l and m are parallel.
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Converse of Same-Side (Consecutive) Interior Angles Theorem
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If two lines in a place are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.
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Converse of Alternate Interior Angles Theorem
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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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∴ JC is parallel to KM
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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, then it is perpendicular to the other.
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if T is perpendicular to K, and K is parallel to L, then T is perpendicular to L.
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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 on line through the point that is parallel to the given line.
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Triangle Sum Theorem
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The sum of the measures of the angles of a triangle is 180.
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Triangle Exterior Angle Theorem
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The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
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Third Angles Theorem
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If two angles of one triangle are congruent to two angles of another triangle, then the third angles of the triangles are congruent.
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Side-Side-Side Postulate
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If the sides of one triangle are congruent to the sides of another triangle, then the triangles are congruent.
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∴ 🔺ABC ≅ 🔺DEF
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Side-Angle-Side Postulate
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If two sides and the angle 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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∴ 🔺ABC ≅ 🔺DEF
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Angle-Side-Angle Postulate
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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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∴ 🔺ABC ≅ 🔺DEF
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Angle-Angle-Side Postulate
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If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.
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∴ 🔺ABC ≅ 🔺DEF
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Corresponding Parts of Congruent Triangles Are Congruent (CPCTC)
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Two triangles are congruent if and only if their corresponding parts 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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Converse of Isosceles Triangle Theorem
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If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
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HL Theorem
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In a pair of RIGHT triangles, if the hypotenuses are congruent and one pair of legs are congruent, then the two triangles are congruent.
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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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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 the 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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