Exploring Addition and Subtraction Theorems in Proofs

What is the main purpose of the addition and subtraction theorems in geometry?

• To determine the perimeter of polygons

• To calculate the area of geometric shapes

• To prove the equality or congruence of segments and angles

• To measure the length of line segments

When should you use the addition theorem in a proof?

• When the segments are perpendicular

• When starting with a small segment and ending with a larger one

• When the angles are obtuse

• When starting with a large segment and ending with a smaller one

In the example given, what is the shared piece that needs to be added to both segments AB and CD?

• Segment BD

• Segment AD

• Segment BC

• Segment AC

What property allows us to state that segment BC is equal to itself?

• Reflexive Property

• Transitive Property

• Associative Property

• Symmetric Property

What is the result when you combine segments AB and BC?

• Segment CD

• Segment AD

• Segment BD

• Segment AC

What is the result when you combine angle 3 with angle 2?

• Angle ACF

• Angle ABF

• Angle ABE

• Angle EBG

Which theorem is used when combining angles to prove congruence?

• Angle Subtraction Theorem

• Angle Multiplication Theorem

• Angle Division Theorem

• Angle Addition Theorem

When should you use the subtraction theorem in a proof?

• When starting with a small segment and ending with a larger one

• When starting with a large segment and ending with a smaller one

• When the segments are parallel

• When the angles are acute

In the subtraction theorem example, what is the piece that needs to be subtracted from both segments AE and BD?

• Segment DE

• Segment BE

• Segment AB

• Segment AD

In the simpler example, what is the result when you combine angles 1 and 2?

• Angle FCD

• Angle ABD

• Angle BCD

• Angle ACD