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Identifying Angles
Proving Lines Parallel (Theorems & Postulates)
Classifying Triangles
Logic
Properties of Equality
100
90 degrees
A right angle's degree is?
100
If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.
Explain the converse of the Corresponding Angles Postulate
100
Add up to 180
The three angles of a triangle add up to?
100
Switch the hypothesis and conclusion
Converse of a conditional
100
a = a
Reflexive Property
200
these angles are nonadjacent interior angles that lie on opposite sides of the transversal.
Describe/Define alternate interior angles
200
If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.
Explain the converse of the alternate interior angles theorem
200
2 sides are the same
Characteristic of an isosceles triangle
200
Switch and negate the statements
Contrapositive of a conditional
200
If a = b; then a + c = b + c
Addition Propety
300
angles lie on the same side of the transversal and between the two lines (drawing)
Describe/define same-side interior angles
300
If two lines and a transversal form side-side interior angles that are supplementary, then the two are parallel.
Explain the converse the same-side interior angles theorem
300
All sides are equal
Characteristics of a equilateral triangle
300
"If and only if"; Symbol: <-->
Biconditional
300
3 X 6 = 6 X 3
Symmetric Property
400
These angles lie on the same side of the transversal and in corresponding positions relative to the two lines (drawing)
Describe/define corresponding angles
400
If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.
Explain the converse of the alternate exterior angles theorem
400
All three sides are different
Characteristics of a scalene triangle
400
The negation of the conjunction of two statements is equivalent to the disjunction of the negations of the two statements
Demorgan's Law
400
6x = 4x + 12; x = 2
Substitution property
500
If two lines and a transversal form same-side exterior angles that are supplementary, then the two lines are parallel.
Explain the converse of the same-side exterior angles theorem
500
An acute, scalene triangle
A triangle with angles less than 90 degrees, with all three sides different
500
If a conditional statement is true, and we know the hypothesis is true... The conclusion must be true.
Law of Modus Tollens
500
if x = y; and y = z, then x = z
Transitive Property