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36 Cards in this Set
- Front
- Back
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SEGMENT ADDITION POSTULATE
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If three points, A, B, and C, are co linear and B is between A and C, then AB+BC=AC
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ANGLE ADDITION POSTULATE
Case 1 |
If point B is in the interior of πAOC, then mπAOB + mπAOC= mπAOC
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ANGLE ADDITION POSTULATE
Case 2 |
If πAOC is a straight angle, then mπAOB+MπBOC = 180
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DEFINITION OF MIDPOINT
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A point B is called a midpoint of a segment AC if B is between A and C and AB=BC
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DEFINITION OF LINEAR PAIR
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A linear pair is a pair of adjacent angles whose non-common sides are opposite rays. In the diagram below, <1 and <2 form a linear pair.
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DEFINITION OF A LINEAR PAIR
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Angles forming a linear pair a supplementary. We can prove this by using the angle addition postulate as well.
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DEFINITION OF A LINEAR PAIR
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If adjacent angles are both congruent and supplementary, then they are both right angles. We can prove this by using the Angle Addition Postulate as well.
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CONGRUENT SUPPLEMENTS THEOREM
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If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.
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CONGRUENT COMPLEMENTS THEOREM
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If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent.
If ,<1 and ,<2 are complementary and ,<3 and <2 are complementary, then <1=<3. |
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ADDITION PROPERTY
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If a=b, then a+c=b+c.
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SUBTRACTION PROPERTY
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If a=b, then a-c=b-c.
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MULTIPLICATION PROPERTY
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If a=b, then ac=bc.
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DIVISION PROPERTY
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If a=b and c=0, then
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REFLEXIVE PROPERTY
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a=a
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SYMMETRIC PROPERTY
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If a=b, then b=a.
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TRANSITIVE PROPERTY
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If a=b and b=c, then a=c.
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SUBSTITUTION PROPERTY
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If a=b, then b can replace a in any equation.
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DISTRIBUTIVE PROPERTY
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a(b+c)=ab+bc
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COMMUTATIVE PROPERTY OF ADDITION
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a+b=b+a
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COMMUTATIVE PROPERTY OF MULTIPLICATION
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ab=ba
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ASSOCIATIVE PROPERTY OF ADDITION
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(a+b)+c=a+(b+c)
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ASSOCIATIVE PROPERTY OF MULTIPLICATION
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(ab)c=a(bc)
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VERTICAL ANGLES THEOREM
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If x and y are the same measures of a pair of vertical angles, then x=y.
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DEFINITION OF CONGRUENT TRIANGLES
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Triangles are congruent if all three pairs of corresponding angles and corresponding sides are congruent. (Total of 6 congruencies).
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SAS CONGRUENCE POSTULATES
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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 two triangles are congruent.
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LL CONGRUENCE THEOREM
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If the legs of one right triangle are congruent respectively to the legs of another right triangle, then the two triangles are congruent.
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HL CONGRUENCE THEOREM
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If the hypotenuse and a leg of one right triangle are congruent respectively to the hypotenuse and a leg of another right triangles, then the two triangles are congruent.
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ASA CONGRUENCE THEOREM
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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 two triangles are congruent.
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SSS CONGRUENCE THEOREM
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if three sides of one triangle are congruent respectively to three sides of another triangle, then the two triangles are congruent.
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CONVERSE OF THE PYTHAGOREAN
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If the sum of the squares of the lengths of two sides of a triangle equals the square of the third side, then the triangle is a right triangle.
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ISOSCELES TRIANGLE THEOREM
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if two sides of one triangle are congruent, then the angles opposite those sides are also congruent. (*** Every equilateral triangle is also equiangular.)
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CONVERSE OF ISOSCELES TRIANGLE THEOREM
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If two angles of one triangle are congruent, then the sides opposite those angles are also congruent. (***Every equiangular triangle is also equilateral.)
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DEFINITION OF ANGLE BISECTOR
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A line, ray or line segment that divides an angle into two congruent coplanar angles. Its endpoint is at the vertex of the angle vertex.
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DEFINITION OF THE PERPENDICULAR BISECTOR OF SEGMENT
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A line, segment, or ray that is perpendicular to the segment at its midpoint, thereby bisecting the segment into two congruent segments.
In an isosceles triangle, if a ray bisects the vertex angle, then it also bisects the base and is perpendicular to it. |
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PERPENDICULAR BISECTOR THEOREM
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A point lies on the perpendicular bisector of a segment IF AND ONLY IF it is equidistant from the endpoints of the segment.
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EXTERIOR ANGLE THEOREM
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The measure of an exterior angle of a triangle is greater than the measure of either of the nonadjacent interior angles (also called remote interior angles). *We will expand this theorem next chapter
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