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Aleksandr [31]
3 years ago
5

Which statement follows from the given theorem? Theorem: The diagonal of a parallelogram divides it into two congruent triangles

.
A. Diagonals of a parallelogram bisect opposite angles.

B. Consecutive sides of a parallelogram are congruent.

C. Consecutive angles of a parallelogram are congruent.

D. Consecutive angles of a parallelogram are supplementary.
Mathematics
1 answer:
777dan777 [17]3 years ago
6 0

Answer with explanation:

Theorem : The diagonal of a parallelogram divides it into two congruent triangles.

Properties of parallelogram

1. Opposite sides are equal and parallel.

2. Diagonal bisect each other.

3. Opposite Angles are equal.

If you will look at the first three options

A:  Diagonals of a parallelogram bisect opposite angles.→→False(Alternate angles are equal)

B: Consecutive sides of a parallelogram are congruent.→→→False(Opposite sides are congruent)

C: Consecutive angles of a parallelogram are congruent.→→→False(Opposite angles are congruent)

D: Consecutive angles of a parallelogram are supplementary.→→→→True

For,any parallelogram, having vertices , A, B and C and D

Opposite sides are parallel, so

1.∠A + ∠B=180°

2.∠C + ∠B=180°

3.∠C+ ∠D=180°

4. ∠A + ∠D=180°

Option D

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The question is incomplete and without a picture. I found similar question as follows:

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and the angle AEB and the angle CBD have the same measure. What is the value of x?

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Referring to the picture, since ABC and DBE are straight lines and crosses each other at B, the angle DBC and EBA are equal.

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