use the determinant method to find the area of a triangle ABC with vertices at A (1,6) B (4,2) and C (-3,3)

Area of triangle is 12.5

Step-by-step explanation:

We need to use the determinant method to find the area of a triangle ABC with vertices at A (1,6) B (4,2) and C (-3,3)

The formula used is:

We are given:

Putting values and finding area

We take mode of -12.5 i.e. |-12.5| because area can't be negative.

So, Area of triangle is 12.5

step-by-step explanation:

i am not sure sorry : c

∠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.