Triangle abc has vertices at a(0, 5), b(−3, 3), and c(0, −5). classify the triangle according to the side lengths.

Scalene triangle

Step-by-step explanation:

The given triangle has vertices at A(0, 5), B(−3, 3), and C(0, −5).

We use the absolute value method to find the length of AC.

units.

We use the distance formula to get;

units

We use the distance formula to find

units.

The three sides of the triangle are not equal in length.

The triangle is scalene

∠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.