One Step Geometry Proofs

Given: Line l is parallel to line m
Prove: <1 is congruent to <8

• Linear Pair Theorem

• Corresponding Angle Postulate

• Vertical Angle Theorem

• Congruent Supplements Theor

Given: the picture
Prove: Segment PF is congruent to segment FQ

• Segment Addition Postulate

• Definition of Angle Bisector

• Definition of Segment Bisector

• Definition of Midpoint

Given: m<1+m<2=180 degrees
Prove: <1 and <2 are supplementary

• Congruent Supplements Theorem

• Linear Pair Theorem

• Definition of Complementary Angles

• Definition of Supplementary Angles

Given: <1 and <2 are right angles
Prove: <1 is congruent to <2

• Definition of Right Angles

• Right Angle Theorem

• Definition of Congruent Angles

• Definition of Complementary Angles

Given: the picture
Prove: m<AOB+m<BOC=m<AOC

• Definition of Angle Bisector

• Segment Addition Postulate

• Angle Addition Postulate

• Definition of Congruent Angles

Given: AB=DC
Prove: Segment AB is congruent to segment DC

• Definition of Congruent Segments

• Definition of Midpoint

• Definition of Congruent Angles

• Segment Addition Postulate

Given: the picture
Prove: <PSQ and <QSR are a linear pair

• Definition of Supplementary Angles

• Linear Pair Theorem

• Congruent Supplements Theorem

• Definition of a Linear Pair

Given: m<A=180 degrees
Prove: <A is a straight angle

• Definition of Supplementary Angles

• Linear Pair Theorem

• Definition of Straight Angle

• Vertical Angle Theorem

In the given diagram, which lines must be parallel?

• b and a

• c and d

• p and q

• k and m

• Definition of right angle

• Definition of supplementary angles

• Definition of angle bisector

• Definition of midpoint