QuestionIs Jackson correct to conclude that triangles are similar from $\frac{3}{6}=\frac{2}{4}$ ? Explain your reasoning.

Studdy Solution

STEP 1

Assumptions1. The proportion written by Jackson is $\frac{3}{6}=\frac{}{4}$ . . We are asked to determine if this proportion indicates that the triangles are similar.
3. Similar triangles have corresponding sides in proportion.

STEP 2

First, we simplify both sides of the proportion to see if they are equal.
$\frac{}{6}=\frac{1}{2}$ $\frac{2}{4}=\frac{1}{2}$

STEP 3

Now, we compare the simplified proportions.
$\frac{1}{2}=\frac{1}{2}$

STEP 4

Since the simplified proportions are equal, this indicates that the corresponding sides of the triangles are in proportion.

STEP 5

Since the corresponding sides of the triangles are in proportion, this suggests that the triangles are similar.
However, it's important to note that in order to definitively say that the triangles are similar, we would need to know that all corresponding sides are in proportion, not just one pair. Without this information, we cannot conclusively say that the triangles are similar based on the given proportion alone.
Jackson's conclusion that the triangles are similar based on the proportion $\frac{3}{}=\frac{2}{4}$ is not necessarily incorrect, but it is incomplete. He would need to show that all corresponding sides are in proportion in order to definitively say that the triangles are similar.

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