Geometry - Deductive Reasoning
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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?
-
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 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 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?
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The multiplication property of equality states:
If a=b, then ca=cb. - What is the DIVISION PROPERTY OF EQUALITY?
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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?
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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?
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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 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 - 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. - 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.