Find the missing variable for a parallelogram:
a = 25in2
h =
b = 3.4 in
(1in=2.54cm)

The missing variable for a parallelogram:

height (h) ≈ 7.35 in or

height(h) ≈ 18.67 cm

Explanation:

Area of parallelogram is base times the height.

i.,e where A is the area , b is the base and h is the height of the parallelogram respectively.

Given: Area (A) = 25 square in.  and breadth(b) = 3.4  in.

To find the height:

Apply parallelogram;

Substitute the value of A and b in above formula;

Divide by 3.4 to both sides;

Simplify:

7.35294118 in = h

or

h ≈ 7.35 in.

To find height in cm

Use 1 in = 2.54 cm

then, h =18.6764 ≈18.67 cm

Therefore, the height in inches is 7.35 in. (approx)

or the height in cm is; 18.67 cm (approx)

∠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.