What is the length of BC?
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|__| Units

BC = 22

Step-by-step explanation:

This is an isosceles triangle.

2x - 24 = x - 2

2x = x - 2 + 24

2x = x + 22

2x -x = 22

x = 22

x = 22

Step-by-step explanation:

Since ∠ B = ∠ C then the triangle is isosceles with 2 legs congruent , that is

AC = AB , substitute values

2x - 24 = x - 2 ( subtract x from both sides )

x - 24 = - 2 ( add 24 to both sides )

x = 22

∠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.