Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. in δprq, the length of is 8 units. the length of mid-segment xy is units.

From given picture we can see that X is mid point of line PQ

So PQ=2PX

From given picture we can see that Y is mid point of line PR

So PR=2PY

Now consider triangles PRQ and PYX

Sides PQ and PX has same ratio as of sides PR and PY (as calculated above)

angle XPY= angle QPR  (common angle)

Hence triangles PRQ and PYX are similar.

We know that ratio of the sides of similar triangles is always equal so we can write:

Plug the given values QR=8 and PQ=2PX

Hence final answer is XY = 4 units.

∠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.

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step-by-step explanation: