1. pia printed two maps of a walking trail. the length of the trail on the first map is 8 cm. the length of the trail on the second map is 6 cm.
(a) 1 cm on the first map represents 2 km on the actual trail. what is the scale factor from the map to the actual trail? what is the length of the actual trail?
scale factor is 1x2=2
8x2/1=16 length of trail

(b) a landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm. what is the scale factor from the first map to the second map? what are the side lengths of the landmark on the second map? show your work.

Step-by-step explanation:

b) 1- scale factor from the first map to the second map:

 = 1.33

   2- landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm.

Side lengths of the landmark on the second map

Divide the length by scale factor:

side lengths of 3 mm:   = 2.25 mm

side lengths of 4 mm:   = 3.007 mm

side lengths of 5 mm:   = 3.75 mm

∠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.

b