Proofs

Notice: these are modified version of notes provided in class by a teacher.

Proofs - ways to state/prove a conclusion is true based on given information, properties, postulates and theorems.

Property	Example
Reflexive property - identical angles, lines, etc are congruent to each other.
Transitive Property - congruency “transfers”	if ∠A ≅ ∠P and ∠P ≅ ∠T then ∠A ≅ ∠T

Property

Example

Reflexive property - identical angles, lines, etc are congruent to each other.

Transitive Property - congruency “transfers”

if ∠A ≅ ∠P and ∠P ≅ ∠T then ∠A ≅ ∠T

Postulate/Theorem	Example
pythagorean theorem
isosceles triangle theorem
3rd angle theorem	The Third Angle Theorem states that if two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles must also be congruent ∠C and ∠J are congruent because all the others are congruent. Why? - because all triangles have to add up to 180°.
Transversal Properties If two parallel lines are cut by a transversal, then: corresponding angles are congruent alternate Angles are congruent alternate exterior angles are congruent same side interior angles are complementary	angles B₁ and S₁ are congruent angles B₁and S are congruent
Vertical Angles are always congruent