A right triangle has legs measuring 4.5 meters and 1.5 meters. The lengths of the legs of a second right triangle are proportional to the lengths of the legs of the first right triangle. Which of the Triangles in the table below has legs that are in proportion to Leg 1 and Leg 2 of Triangle 1?

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

really really sorry if i'm

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-12 - 5x - 20 = 3x

-12 - 20 - 5x = 3x

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    + 5x   + 5x

-32 = 8x

8         8

- 4= x