In the figure below, the segment is parallel to one side of the triangle. the ratio of 12 to y is 1: 2 1: 3 1: 4 2: 3

Option B. 1 : 3

Step-by-step explanation:

There are two triangles shown in the picture attached ΔABC and ΔCD.

In these triangles sides AB and DE are parallel and BC is transverse line so ∠ABC = ∠EDC (corresponding angles)

Similarly AC is transverse to parallel lines AB and DE, so ∠BAC = ∠DEC (corresponding angles)

∠ACB is common in both the triangles.

Therefore ΔABC and ΔDEC are similar.

We know in similar triangles corresponding sides are in the same ratio.

Therefore ratio of y and 12 is equal to 3 : 1

Or ratio of 12 to y is 1 : 3

Option B is the answer.

Option 2.

Step-by-step explanation:

In the figure below, the segment is parallel to one side of the triangle.

Given: BC║DE

In triangle ABC and ADE,

              (Reflexive property)

               (Corresponding angles)

By AA property of similarity,

Corresponding parts of similar triangle are proportional.

The ratio of 12 to y is 1:3. Therefore, the correct option is 2.

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step-by-step explanation: