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### 30 Cards in this Set

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 What is the MIDPOINT THEOREM? This theorem states: If M is the midpoint of line segment AB, then AM=1/2AB; MB=1/2AB. What is the ANGLE BISECTOR THEOREM? This theorem states: If ray BX is the bisector of angle ABC, then MEASURE OF ANGLE ABX = HALF OF THE MEASURE OF ANGLE ABC & THE MEASURE OF ANGLE XBC = HALF OF THE MEASURE OF ANGLE ABC. What is DEDUCTIVE REASONING? Proving statements by reasoning from accepted postulates, theorems, and given information. What is the DISTRIBUTIVE PROPERTY OF EQUALITY? The distributive property of equality states: a(b+c)=ab+ac. What is the ANGLE BISECTOR THEOREM? The angle bisector theorem states: If ray BX is the bisector of angle ABC, then the measure of angle ABX = half of the measure of angle ABC, and the measure of angle XBC = half of the measure of angle ABC. What are COMPLEMENTARY ANGLES? Complementary angles are two angles whose measures have the sum of 90. What are SUPPLEMENTARY ANGLES? Supplementary angles are two angles whose measures have the sum of 180. What are VERTICAL ANGLES? Vertical Angles are two anglessuch that the sides of one angle are opposite rays to the sides of the other angle. What is an IF-THEN STATEMENT? An if-then statement is a statement whose basic form is "if p then q." Statement p is the hypothesis and statement q is the conclusion. What is the CONVERSE OF A CONDITIONAL? The converse of the statement "If p, then q" is the statement "If q, then p" What is a COUNTEREXAMPLE? A counterexample is an example used to prove that an if-then statement is false. For that counterexample, the hypothesis is true and the conclusion is false. What is a BICONDITIONAL? A biconditional is a statement that contains the words "if and only if." What is the ADDITION PROPERTY OF EQUALITY? The addition property of equality states: If a=b and c=d,then a+c=b+d What is the SUBTRACTION PROPERTY OF EQUALITY? The subtraction property of equality states: If a=b and c=d, then a-c=b-d What is the MULTIPLICATION PROPERTY OF EQUALITY? The multiplication property of equality states: If a=b, then ca=cb. What is the DIVISION PROPERTY OF EQUALITY? The division property of equality states: If a=b and c can't = 0, then a/c=b/c What is the SUBSTITUTION PROPERTY OF EQUALITY? The substitution property of equality states: If a=b, then either a or b can be substituted for the other in any equation (or inequality). What is the REFLEXIVE PROPERTY OF EQUALITY? The reflexive property of equality states: a=a. What is the SYMMETRIC PROPERTY OF EQUALITY? The symmetric property of equality states: If a=b, then b=a. What is the TRANSITIVE PROPERTY OF EQUALITY? The transitive property of equality states: If a=b and b=c, then a=c. What is the REFLEXIVE PROPERTY OF CONGRUENCE? The reflexive property of congruence states: segment DE is congruent to segment DE OR angle D is congruent to angle D. What is the SYMMETRIC PROPERTY OF CONGRUENCE? The symmetric property of congruence states: If segment DE is congruent to segment FG, then segment FG is congruent to segment DE. OR If angle D is congruent to angle E, then angle E is congruent to angle D. What is the TRANSITIVE PROPERTY OF EQUALITY? The transitive property of equality states: If segment DE is congruent to segment FG and segment FG is congruent to segment JK, then segment DE is congruent to JK. OR If angle D is congruent to angle E and angle E is congruent to angle F, then angle D is congruent to angle F PERPENDICULAR LINES Two lines that intersect to form right angles. Complete the theorem about Perpendicular lines: If two lines are perpendicular... then they form congruent adjacent angles. Complete the theorem about perpendicular lines: If twolines form congruent, adjacent angles... then the lines are perpendicular. Complete the theorem about perpendicular lines: If the exterior sides of two adjacent acute angles are perpendicular, then the angles are perpendicular. What five parts are in a proof of a theorem? 1) Statement of the theorem. 2) A diagram that illustrates the given information. 3) A list in terms of the figure, of what is given. 4) A list in terms of the figure, of what you are to prove. 5) A series of statements and reasons that lead from the given information to the statement that is proved. CONGRUENT SUPPLEMENTS THEOREM If two angles are supplements of congurent angles (or the same angle), then the two angles are congruent. CONGRUENT COMPLEMENTS THEOREM If two angles are complements of congruent angles (or the same angle), then the two angles are congruent.