Reasons in Triangle Proofs

The five ways to prove triangles congruent

SAS, SSS, ASA, AAS, and HL

what kind of line splits an angle into two equal angles

an angle bisector

What shortcuts can you not take when proving triangles congruent

SSA and AAA

What does CPCTC stand for

Corresponding Parts of Congruent Triangles are Congruent

What theorem does this picture demonstrate?

Vertical Angles theorem

what property proves that DB is equal to BD?

Reflexive property

Assuming the two horizontal lines are perpendicular, how can we prove the two highlighted angles congruent?

Parallel lines cut by a transversal form congruent alternate interior angles

Assuming the two horizontal lines are perpendicular, how can we prove the two highlighted angles congruent?

Parallel lines cut by a transversal form congruent alternate exterior angles

What theorem is this

Isosceles triangle theorem

∠ABC≅∠WXY, and ∠CBD≅∠YXZ. What reason proves that ∠ABD≅∠WXZ?

Congruent angles added to Congruent angles form congruent angles

∠ABD≅∠WXZ, and ∠CBD≅∠YXZ. What reason proves that ∠ABC≅∠WXY?

Congruent angles removed from congruent angles form congruent angles

A point that divides a segment into two congruent segments.

a Midpoint

what divides an angle into two congruent angles.

an Angle Bisector

Definition of Complementary Angles

Two angles whose measures add up to 90 degrees.

Definition of Supplementary Angles

Two angles whose measures add up to 180 degrees.

Why are these angles congruent?

All right angles are congruent.

Definition of Linear Pairs

A pair of adjacent angles whose non-common sides form a straight line.

Perpendicular lines form what kind of angle?

Right angles

∠1≅∠4, and ∠1≅∠5. What property is used to prove ∠4 ≅∠5?

Transitive property