Question

2 multiple choice 6 points
nrtw is a parallelogram whose diagonals intersect at point b. some measurements are given.
nw = 3x - 10, tb = 7x + 2, bw = 2x - 12, tw = 4x + 5, wr = 300
which property can we use to find the value of x.

• diagonal bisect each other. make both diagonals equal to each other.
• opposite angles are congruent.
• diagonal bisect each other. multiply the half diagonal by 2 to make it equal to the other diagonal.
• opposite sides are congruent.

clear my selection

Explanation:

In a parallelogram, the diagonals bisect each other. This means that the point of intersection (B) divides each diagonal into two equal parts. So, if we have a half - diagonal (like TB or BW), to get the length of the whole diagonal, we multiply the length of the half - diagonal by 2. For example, if TB is a half - diagonal of one diagonal, then 2×TB should be equal to the length of that diagonal, and we can set up an equation with the other diagonal's expression (or part of it) to solve for x.

• The first option is incorrect because we don't set the two diagonals equal directly (we use the fact that half of one diagonal times 2 equals the other diagonal or its half).
• The second option is incorrect because opposite angles being congruent has nothing to do with finding x from the given diagonal and side - like expressions.
• The fourth option is incorrect because opposite sides being congruent doesn't relate to the diagonal expressions given (NW, TB, BW etc. are related to diagonals, not opposite sides).

Answer:

C. Diagonal bisect each other. Multiply the half diagonal by 2 to make it equal to the other diagonal.