Geometric Theorems and Proofs

Why is it helpful to sketch a diagram when writing certain proofs?

• To make the proof look more professional

• To waste time

• To visualize the problem and understand the relationships between geometric figures

• To confuse the reader

What is the purpose of the Linear Pair Postulate in geometry?

• To justify the statement that angles that form linear pairs are complementary

• To find the graph of an equation

• To prove the third angle Theorem

• To justify the statement that angles that form linear pairs are supplementary

How can you prove step #2?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

How can you prove step #4?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

Fill in the blanks to complete the geometric proof:

• ∠PQR = 38; B: Definition of Complementary Angles; C: Subtraction

  Property of Equality

• ∠PQR = 38; B: Definition of Supplementary Angles; C: Reflexive Property

• ∠PQR = 38; B: Definition of Vertical Angles; C: Transitive Property

• ∠PQR = 38; B: Definition of Complementary Angles; C: Substitution

Fill in the blanks to complete the geometric proof:

• ∠PQR = 38; B: Definition of Complementary Angles; C: Subtraction

  Property of Equality

• ∠PQR = 38; B: Definition of Supplementary Angles; C: Reflexive Property

• ∠PQR = 38; B: Definition of Vertical Angles; C: Transitive Property

• ∠PQR = 38; B: Definition of Complementary Angles; C: Substitution

What reason justifies statement #2?

• Definition of Midpoint

• Transitive Property

• Addition Property

• Segment Addition Postulate

• Substitution Property

What is the "reason" for step 5 of the proof?

• Angle Bisector Theorem

• Reflexive property

• CPCTC Theorem

• Proof

How can you prove step #5?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

Identify the  missing statement or reason

• Given

• Vertical Angles Theorem

• Definition of Angle Bisector

• Alternate Interior Angles Theorem