Select the correct answer.
Given:
Prove:
Two parallel lines passing the vertices with red line r at points (c, d) at (2, 10) and (O, b) at (0, 6) and blue line s intercepts (c, O) at (2, 0) and (O, a) at (0, minus 4)
Statements Reasons
1.
given
2.
?
3. distance from
to
equals the distance from
to
definition of parallel lines
4.
application of the distance formula
5.
substitution property of equality
6.
inverse property of addition
7.
substitution property of equality
The table shows the proof of the relationship between the slopes of two parallel lines. What is the missing reason for step 2?
A.
application of the distance formula
B.
Pythagorean theorem
C.
transitive property
D.
application of the slope formula
The missing reason for step 2 is B. Pythagorean theorem.
The missing reason for step 2 is B. Pythagorean theorem.
To understand why, let's think about what the Pythagorean theorem states. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this specific context, the distance from point (c, d) to (2, 10) and the distance from point (0, b) to (0, 6) represent the two legs of a right triangle. By using the Pythagorean theorem, we can confirm that the distance between these two points is equal to the square root of the sum of the squares of the differences in the x and y coordinates.
Therefore, step 2 involves using the Pythagorean theorem to find the distance between the two parallel lines passing through the given points. This distance will be later used to prove that the lines are parallel. Hence, the correct answer is B. Pythagorean theorem.