Geometry Proofs (Theorems + Axioms) 😔

Def of congruent segment

2 segments are congruent if and only if they have the same length (measure)

Def of bisect

to divide into congruent parts

Def of segment bisector

line/part of a line that intersects a segment at its midpoint and divedes the segment into two congruent parts

Segment(or angle) addition axiom

The whole is equal to the sum of its parts

Def of perpendicular lines

Lines that intersect to form right angles

Def of perpendicular bisector

A line that is perpendicular to a line segment at its midpoint

Def of congruent angles

angles that have the same measure

Def of angle bisector

ray that divides an angle into two congruent parts

Def of adjacent angles

angle pairs that have:
1) a common vertex

2) a common side

3) no interior points in common

Def of complementary

2 angles are complementary if and only if the sum of their measures is 90 degrees

Def of supplementary

2 angles are supplementary if and only if the sum of their measures is 180 degrees

Def of perpendicular pairs

2 adjacent angles whose non-common sides are perpendicular

Supplement axiom

the angles of a linear pair are supplementary

Complement axiom

the angles of a perpendicular pair are complementary

If 2 angles are supplementary to the same angle then they are congruent

SHORT VERSION!!: Supplements of the same angle are congruent

if 2 angles are supplementary to congruent angles then they are congruent

SHORT!!: supplements of congruent angles are congruent

If 2 angles are commplementary to the same angle then they are congruent

SHORT!!: complements of the same angle are congruent

If 2 angles are complementary to congruent angles then they are congruent

SHORT!!: Complements of congruent angles are congruent

If 2 angles are right angles then they are congruent to each other

SHORT!!: All right angles are congruent

If 2 angles are congruent and supplementary then they are right angles

YOU GOT THIS!!

If two lines intersect to form congruent adjacent angles then the lines are perpendicular

ACE THIS TEST YAY!!

If 2 lines are perpendicular then they intersect to form congruent adjacent angles

OKAY SMARTY!

Vertical angles are congruent

KEEP STUDYING!!

GRAWS (Small —> Big)

1. Given

2. Reflexive property

3. Addition property

4. Segment addition axiom(W)

5. Segment addition axiom

6. Substitution property

GWSRS

1. Given

2. Segment addition axiom(W)

3. Segment addition axiom

4. Substitution property

5. Reflexive property

6. Subtraction property

Def of midpoint of a line segment

a point that divides the segment into 2 congruent points