Question

Consider the paragraph proof.

Given: D is the midpoint of AB, and E is the midpoint of AC.
Prove:DE = One-halfBC

On a coordinate plane, triangle A B C is cut by line segment D E. Point D is the midpoint of side A B and point E is the midpoint of side A C. Point A is at (2 b, 2 c), point E is at (a + b, c), point C is at (2 a, 0), point B is at (0, 0), and point D is at (b, c).

It is given that D is the midpoint of AB and E is the midpoint of AC. To prove that DE is half the length of BC, the distance formula, d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot, can be used to determine the lengths of the two segments. The length of BC can be determined with the equation BC = StartRoot (2 a minus 0) squared + (0 minus 0) squared EndRoot, which simplifies to 2a. The length of DE can be determined with the equation DE = StartRoot (a + b minus b) squared + (c minus c) squared EndRoot, which simplifies to ________. Therefore, BC is twice DE, and DE is half BC.

Which is the missing information in the proof?

a
4a
a2
4a2

Answer 1

The answer can be found from the last lines itself.

We have found:

DE = √{(a + b - b)² + (c - c)²}

= √(a² + 0²)

= √(a²)

= a

So, DE simplifies to a.

Missing information is a.

Note: This proof is done here using coordinate geometry. The line parallel to the base of a triangle, bisecting the other two sides is half of the base.

Answer 2

Answer:

The information that is missing in this proof is a

Step-by-step explanation:

right on edge