Geometric Proof

Choose the correct definition, postulate, or theorem for the following statement

• Definition of Midpoint

• Definition of Segment Addition

• Vertical Angle Theorem

• Definition of Supplementary

• Definition of Colinear

• Given

• Vertical angles are congruent.

• Definition of linear pair.

• Definition of adjacent angles.

Given: Samuel's cake slice ∠LAN = 30⁰, the decoration angle ∠1 = 15⁰
Prove: The knife cut AM bisects ∠LAN
Step 1: ∠LAN = 30⁰ 
Step 2: ∠1 + ∠2 = ∠LAN
Step 3: ∠1 + ∠2 = 30⁰
What is the justification for Step 3?

• Given

• Substitution

• Angle addition postulate

• Definition of congruent angles

Noah is looking at a map and notices that the distance from point A to point E plus the distance from point E to point C is equal to the distance from point A to point C. What reason allows us to say that AE+EC=AC?

• Angle Addition Postulate

• Segment Addition Postulate

• Linear Pair Theorem

• Definition of Midpoint

• Angle Addition Postulate

• Segment Addition Postulate

• Linear Pair Theorem

• Definition of Midpoint

• definition of straight angle

• definition of line segment addition

• definition of supplementary angles

• definition of midpoint

Abigail noticed that the fence post BD is part of both her garden and Mason's garden, meaning it is congruent to itself. What property is this an example of?

• Substitution

• Commutative

• Reflexive

• Transitive

Reorder the reasons for the proof.

• Given

• Transitive Property of Congruence

• Definition of midpoint

Isla and Jackson are looking at a pair of crossing streets. Isla notes that the angles where the streets intersect are vertical angles. What should Jackson conclude by the vertical angles theorem?

• undefined and undefined are right angles.

Angles 3 and 5 are congruent because they are ______.