Converse Parallelogram Proofs Practice

Question

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Question
Use the image to answer the question.

A parallelogram has vertices upper R, upper S, upper U, and upper T. Opposite vertices are connected via diagonal lines that intersect at an interior point labeled upper V. The lines formed between each vertex and upper V are labeled.

If quadrilateral RSTU
is a parallelogram, what are the lengths of the diagonals of the figure?

(1 point)
Diagonal RT
is equal to
and diagonal SU
is equal to
.

Answer 1

In a parallelogram, the diagonals bisect each other. This means that the lengths of the segments created by the intersection of the diagonals are equal.

Let’s say the lengths of the segments from point V to the vertices are as follows:

• RV = a
• VS = b
• UV = c
• VT = d

From the property of parallelograms, we know that:

1. Diagonal RT is composed of segments RV and VT, which can be expressed as: \[ RT = RV + VT = a + d \]

2. Diagonal SU is composed of segments SV and UV, which can be expressed as: \[ SU = SV + UV = b + c \]

If you have the specific lengths of segments RV, VS, UV, and VT, you can substitute those values to find the exact lengths of the diagonals RT and SU. Without the specific measurements, I can’t provide the exact values. Please plug in the values that correspond to your image of the parallelogram, and you can find the lengths of the diagonals accordingly.