1.3 Mathematical Proofs

Question 1

What are congruent angles?

Answer 1

Angles that have the same measurement

Question 2

What is an Indirect Proof?

Answer 2

An Indirect Proof is an argument that uses a contradiction to prove a statement true.

Question 3

What is a Direct Proof?

Answer 3

A Direct Proof is a statement that establishes the truth of a conjecture using a logical sequence of statements.

Question 4

True or False: The Axiomatic system is a Direct Proof

Answer 4

True! It’s logical and not freaking backwards 😤

Question 5

What are the 4 properties of Equality & Congruence

Answer 5

1. Reflexive Property
2. Symmetric Property
3. Transitive Property
4. Substitution Property

Question 6

What is the Reflexive Property of Congruence?

Answer 6

Any value is equal to itself: x=x

Question 7

What is the Symmetric Property of Congruence?

Answer 7

If x=y then y=x as well

Question 8

What is the Transitive Property of Congruence

Answer 8

If x=y and y=z then x also equals z (x=z)

Question 9

What is the Substitution Property of Congruence?

Answer 9

If a=b then “a” can be used as a substitute for “b” in any equation and vice versa

Question 10

What are the four Algebraic Properties?

Answer 10

1. Addition Property of Equality
2. Subtraction Property of Equality
3. Multiplication Property of Equality
4. Division Property of Equality

Question 11

What is the Addition Property of Equality?

Answer 11

If x=y then x+a = y+a

Question 12

What is the Subtraction Property of Equality?

Answer 12

If x=y then x-a = y-a

Question 13

What is the Multiplication Property of Equality?

Answer 13

if x=y then ax = ay

Question 14

What is the Division Property of Equality?

Answer 14

if x=y then x÷a = y÷a

Question 15

What is the Angle Addition Property?

Answer 15

if B is a point on the interior of ∠AOC, then the measure of ∠AOC is equal to the sum of ∠AOB and ∠BOC

Question 16

What is the Segment Addition Property?

Answer 16

If B is a point on segment AC, then the length of AC is the sum of AB and BC

Question 17

What is the Linear Pair Theorem?

Answer 17

If two angles form a linear pair, then their angles are supplementary

Question 18

What is the Congruent Angles Theorem?

Answer 18

If two angles are supplementary (in an intersection) to the same angle then they are congruent

Question 19

What is the Congruent and Supplementary Angles Theorem?

Answer 19

If two congruent angles are supplementary (equal 180°) then their angles are 90°

Question 20

What is the Vertical Angles Theorem?

Answer 20

When two lines intersect they form vertical angles. Vertical angles are congruent to each other!

Question 21

What is the Congruent Supplements Theorem?

Answer 21

Since two intersecting angles are supplementary to the same angle, they are congruent.