Exploring Algebraic Proofs in Geometry

What is the main focus of Chapter 2 Section Five?

• Geometric transformations

• Calculus fundamentals

• Algebraic proofs

• Trigonometric identities

What is deductive reasoning?

• The process of guessing based on intuition

• The process of reasoning logically from given facts to a conclusion

• The process of solving equations without any rules

• The process of proving statements using experiments

Which property allows you to add the same value to both sides of an equation?

• Division property of equality

• Addition property of equality

• Multiplication property of equality

• Subtraction property of equality

What is the commutative property of addition?

• a * b = b * a

• a - b = b - a

• a + b = b + a

• a / b = b / a

What is the first step in solving the equation 4m - 8 = -4?

• Multiply both sides by 4

• Subtract 8 from both sides

• Add 8 to both sides

• Divide both sides by 4

Which property justifies the step of dividing both sides of an equation by the same number?

• Division property of equality

• Multiplication property of equality

• Subtraction property of equality

• Addition property of equality

What is the segment addition postulate?

• The product of two segments is equal to the product of their lengths

• The sum of the lengths of two segments is equal to the length of the third segment

• The distance from one point to another is the sum of the distances of the segments in between

• The sum of the angles in a triangle is 180 degrees

Which property allows you to substitute one value for another in an equation?

• Transitive property of equality

• Reflexive property of equality

• Substitution property of equality

• Symmetric property of equality

What does the reflexive property of congruence state?

• If a figure is congruent to another, the second figure is congruent to the first

• If a figure is congruent to itself, it is also congruent to another figure

• A figure is always congruent to itself

• If two figures are congruent to a third figure, they are congruent to each other

Which property justifies the statement: If AB is congruent to CD and CD is congruent to EF, then AB is congruent to EF?

• Reflexive property of congruence

• Substitution property of congruence

• Transitive property of congruence

• Symmetric property of congruence