Question

Select the correct answer. Given: ∆ABC Prove: A midsegment of ∆ABC is parallel to a side of ∆ABC. Statement Reason 1. Define the vertices of ∆ABC to have unique points A(x1, y1), B(x2, y2), and C(x3, y3). given 2. Let D be the midpoint of and E be the midpoint of . defining midpoints 3. definition of midpoints 4. slope of slope of definition of slope 5. slope of = slope of Transitive Property of Equality 6. definition of parallel lines 7. Let F be the midpoint of . defining a midpoint 8. definition of midpoint 9. slope of slope of definition of slope 10. 11. definition of parallel lines 12. Similarly, is parallel to . steps similar to steps 1−11 What is the missing step in this proof? A. Statement: slope of = slope of Reason: definition of slope B. Statement: slope of = slope of Reason: Transitive Property of Equality C. Statement: DF = BC Reason: Corresponding sides of congruent triangles are congruent. D. Statement: ∆A

Answer 1

Concept:

If two numbers are equal and the second number is equal to the third number, then the first number is also equal to the third number, according to the transitive property of equality. The transitive property of equality states that if a, b, and c are three quantities, and if an is connected to b by some rule and b is related to c by the same method, then a and c are related to each other by the same rule.

Find:

The missing statement.

Solution:

The slope of DF = slope of BC, according to the transitive property of equality.

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Answer 2

We learned that the transitive property of equality tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing.

The formula for this property is if

a = b

and b = c,

then a = c.

Hence according to the transitive property of equality, it is can be considered that:-

The slope of DF = slope of BC,

Ans :-  Transitive Property of Equality C. Statement: DF = BC Reason: Corresponding sides of congruent triangles are congruent.

The slope of DF = slope of BC,

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