Segment bd is an altitude of triangle abc. find the area of the triangle. triangle abc with altitude bd is shown. point a is at 2, 1. point b is at negative 1, 4. point c is at 2, 6. point d is at 2, 4. a.7.5 b.9.5 c.10 d.15

A. 7.5

Step-by-step explanation:

In triangle ABC, BD is the altitude of the triangle which means BD is its height and AC is its base.

We know that B(-1,4) and D(2,4), therefore we can find height BD using the distance formula:

BD =

Now, we will find the base AC:

Area of the triangle = 1/2 * base * height

Area of ABC = 1/2 * AC * BD = 1/2 * 5 * 3 = 7.5

Therefore, the area of ABC is 7.5.

∠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.

g

step-by-step explanation: