name the def, property, postulate, or theorem that justifies each statement

Question

if line AB is congruent to line CD, then AB+EF=CD+EF

If line AB is congruent to line XY then XY is congruent to AB

if x(y+z)=a, then xy+xz=a

if two angles are vertical then they are congruent

if angle 1 and angle 2 are right angles then angle 1 is congruent to angle 2

Answer 1

Hi, Haroron,

In the first line, you are adding the same segment to two line segments that are congruent. This is normally the Addition Property of Equality.

The second line is the Symmetric Property.

The third line is the Distributive Property of Multiplication.

The fourth line is the Definition of Vertical Angles.

The fifth line is usually stated as All right angles are congruent.

Each of these should be listed in your book. If they are not, look for something similar.

I hope this helps!

Best, Karen