Proof
Reasons
The names shown in green are okay to use directly as
proof reasons. For the other
definitions, postulates, properties, and
theorems, you should use the descriptions shown.
Miscellaneous Reasons Given Simplification Basic Properties of Numbers (Info Sheet #13) Commutative Associative Distributive Algebraic Properties of
Equality (Info Sheet #13) Addition Subtraction Multiplication Division Substitution Equivalence Properties of
Equality and Congruence (Info Sheet #13) Reflexive Symmetric Transitive Definition of
Perpendicular Lines (Info Sheet #3) Two lines
intersecting at a right (90°) ∠ are ⊥. Two ⊥ lines intersect at a right (90°) ∠. Definition of
Segment Midpoint (Info Sheet #3) The
midpoint of a segment is the point that divides the segment into two ≅ segments. Definition of
Segment Bisector (Info Sheet #3) A segment
bisector (a point, ray, line, segment, or plane) intersects a segment at its
midpoint (dividing it into two ≅ segments). Segment Congruence Postulate (Info Sheet #3) Two
segments of the same length are ≅. Two ≅ segments are the same length. Segment Addition
Postulate (Info Sheet #3) If point R
is between points P and Q on a line, then PR + RQ = PQ. Definition of Right
Angle (Info Sheet #4) A right ∠ is an ∠ with a
measure of exactly 90°. Definition of Angle
Bisector (Info Sheet #4) An ∠ bisector (a ray or line)
divides an ∠ into two ≅ ∠s. Angle Congruence Postulate (Info Sheet #4) Two ∠s with = measures are ≅. Two ≅ ∠s have = measures. Angle Addition
Postulate (Info Sheet #4) If point S is in the interior of ∠PQR, then m∡PQS + m∡SQR = m∡PQR. Definition of
Supplementary Angles (Info Sheet #4) Two ∠s adding
to 180° are supplementary. Supplementary
∠s add up to 180°. Definition of
Complementary Angles (Info Sheet #4) Two ∠s adding
to 90° are complementary. Complementary
∠s add up to 90°. Linear Pair Property (Info Sheet #4) Two ∠s forming
a linear pair are supplementary. Definition of Right
Triangle (Info Sheet #5) A right ∆
is a ∆ that contains a right (90°) interior ∠. Vertical Angles Theorem (Info Sheet #5) Vertical ∠s are ≅. Triangle Sum Theorem (Info Sheet #5) Sum of 3
interior ∆ ∠s = 180°. Overlapping
Segments Theorem (Info Sheet #9) Given points A, B, C, D
on a line (in that order): If AB = CD, then AC = BD. Given points A, B, C,
D on a line (in that order): If AC = BD, then AB = CD. Overlapping Angles
Theorem (Info Sheet #9) Given ∠AOD
with points B and C in its interior: If m∡AOB = m∡COD, then m∡AOC = m∡BOD. Given ∠AOD with points B and C in its interior: If m∡AOC = m∡BOD, then m∡AOB = m∡COD. Corresponding Angles Postulate
and Converse (Info Sheet #11 & Info Sheet #12) Transversal
with ∥ lines → ≅ corresponding ∠s. Transversal
with ≅ corresponding ∠s → ∥ lines. Alternate Exterior Angles
Theorem and Converse (Info Sheet #11 & Info Sheet #12) Transversal
with ∥ lines → ≅ alternate exterior ∠s. Transversal
with ≅ alternate exterior ∠s → ∥ lines. Alternate Interior Angles
Theorem and Converse (Info Sheet #11 & Info Sheet #12) Transversal
with ∥
lines →
≅ alternate interior ∠s. Transversal
with ≅ alternate interior ∠s → ∥ lines. Same-Side Interior Angles
Theorem and Converse (Info Sheet #11 & Info Sheet #12) Transversal
with ∥ lines → supplementary
same-side interior ∠s. Transversal
with supplementary same-side interior ∠s → ∥ lines. Perpendicular and Parallel
Lines (Info Sheet #12) Two
coplanar lines ⊥ to same line → ∥ lines. Two
coplanar lines ∥ to same line → ∥ lines. Miscellaneous Theorem Multiple
adjacent ∠s forming a line → sum of ∠s = 180°. (Info Sheet #12) Parallel Postulate (Info Sheet #15) Given a
line and a point not on the line, there is exactly one line through the given
point that is parallel to the given line. Perpendicular
Postulate (Info Sheet #15) Given a
line and a point not on the line, there is exactly one line through the given
point that is perpendicular to the given line. Miscellaneous Theorem Two ≅ and
supplementary ∠s are right (90°) ∠s. (Info Sheet #15) Right Angle Congruence Theorem (Info Sheet #15) All right
(90°) ∠s are ≅. Congruent
Supplements/Complements Theorems (Info Sheet #16) Two ∠s are ≅ if they are supplements of the
same or ≅ ∠s. Two ∠s are ≅ if they are complements of the
same or ≅ ∠s. |