1.3 Mathematical Proofs Flashcards
What are congruent angles?
Angles that have the same measurement
What is an Indirect Proof?
An Indirect Proof is an argument that uses a contradiction to prove a statement true.
What is a Direct Proof?
A Direct Proof is a statement that establishes the truth of a conjecture using a logical sequence of statements.
True or False: The Axiomatic system is a Direct Proof
True! It’s logical and not freaking backwards 😤
What are the 4 properties of Equality & Congruence
- Reflexive Property
- Symmetric Property
- Transitive Property
- Substitution Property
What is the Reflexive Property of Congruence?
Any value is equal to itself: x=x
What is the Symmetric Property of Congruence?
If x=y then y=x as well
What is the Transitive Property of Congruence
If x=y and y=z then x also equals z (x=z)
What is the Substitution Property of Congruence?
If a=b then “a” can be used as a substitute for “b” in any equation and vice versa
What are the four Algebraic Properties?
- Addition Property of Equality
- Subtraction Property of Equality
- Multiplication Property of Equality
- Division Property of Equality
What is the Addition Property of Equality?
If x=y then x+a = y+a
What is the Subtraction Property of Equality?
If x=y then x-a = y-a
What is the Multiplication Property of Equality?
if x=y then ax = ay
What is the Division Property of Equality?
if x=y then x÷a = y÷a
What is the Angle Addition Property?
if B is a point on the interior of ∠AOC, then the measure of ∠AOC is equal to the sum of ∠AOB and ∠BOC
What is the Segment Addition Property?
If B is a point on segment AC, then the length of AC is the sum of AB and BC
What is the Linear Pair Theorem?
If two angles form a linear pair, then their angles are supplementary
What is the Congruent Angles Theorem?
If two angles are supplementary (in an intersection) to the same angle then they are congruent
What is the Congruent and Supplementary Angles Theorem?
If two congruent angles are supplementary (equal 180°) then their angles are 90°
What is the Vertical Angles Theorem?
When two lines intersect they form vertical angles. Vertical angles are congruent to each other!
What is the Congruent Supplements Theorem?
Since two intersecting angles are supplementary to the same angle, they are congruent.
