In the picture, lines a, b, and c are parallel.
Simon and Adara set up correct but different proportions that can be used to find the unknown segment lengths in the diagram.
Use the drop-down menus to complete the proportions.
Simon’s Proportion
X + 4
=
7x – 4
Adara’s Proportion
3
=
8
To complete the proportions set up by Simon and Adara, we first need to understand the relationships between the segments created by the parallel lines.
### Simon’s Proportion:
1. Set up the proportion: From the information given, we have:
[
frac{X + 4}{7x – 4}
]
2. Complete the proportion: The completed Simon’s proportion can be in the form of corresponding segments:
[
frac{X + 4}{A} = frac{B}{7x – 4}
]
Where (A) and (B) represent segments that correspond according to the Triangle Proportionality Theorem, which states that the ratio of lengths of two segments is equal to the ratio of the lengths of the segments along the transversal.
### Adara’s Proportion:
1. Set up the proportion: The information provided suggests the following proportion:
[
frac{3}{8}
]
2. Complete the proportion: Similar to Simon, Adara’s proportion can be represented as:
[
frac{3}{8} = frac{C}{D}
]
Where (C) and (D) again represent corresponding segments associated with the parallel lines.
Given that I don’t have specific values for (A), (B), (C), or (D