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34 Cards in this Set
- Front
- Back
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conjecture
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educated guess based on observations
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inductive reasoning
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looking at patterns and making conjectures
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counterexample
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proves a conjecture false
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ray
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part of a line with an initial point
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opposite rays
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two rays with the same initial point that go in oppoisite directions
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postulate
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an unproven, accepted rule
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conditional statement
p -> q |
a statement that includes a hypothesis and conclusion
"if", ... "then"... |
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converse statement
q -> p |
reverses conditional statement
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inverse statement
~p -> ~q |
negates the conditional statement's hypothesis and conclusion
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contrapositive statement
~q -> ~p |
negates converse statement
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biconditional statement
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"if and only if"
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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, 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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addition/subtraction property
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if a=b, then a+c = a+b
if a=b, then a-c = a-b |
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multiplication property
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if a=b, a x b=a x c, and if c doesnt = 0, a/c = b/c
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substitution property
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if a=b, a can be replaced by b in any equation or expression
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distributive property
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a(b+c)=ab+ac
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equilateral
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all congruent sides
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isosceles
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two or more congruent sides
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scalene
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no congruent sides
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adjacent sides
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two sides of a polygon with a common vertex
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hypotenuse
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side of the right triangle opposite the right angle
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HL of RT TRIANGLES
[hypotenuse-leg] |
If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then triangles are congruent
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median
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segment in a triange that goes from a vertex to the midpoint of the side opposite
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centroid
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point of concurrency for medians
[always inside the triangle |
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altitude
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segment in a triangle with endpoints at a vertex and on an opposite side which creates perpendicular lines
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orthocenter
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point of concurrency for altitudes of a triangle
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perpendicular bisector
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intersects a segment at its midpoint and is perpendicular to the segment
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Angle Bisector Theorem
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If a point is on the bisector of an angle, then it is equidistant from the sides of the angle
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concurrent lines [rays/segments]
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three or more lines interseting at only one point
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incenter
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point of concurrency for angle bisectors
[inside for all three] |
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midsegment of a triangle
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segment that connects two midpoints of a triangle
it is parallel and half of the third side |
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parallelogram
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polygon in which both sides of opposite sides are parallel to eachother
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