Solve the following problem:
Which triangles are similar? Which sides are proportional?

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  ΔA₁CA ~ ΔBCB₁

Step-by-step explanation:

The triangles share angle C. The 30° angles are also congruent, so the triangles are similar by the AA theorem.

It is convenient to name the similar triangles by matching the similar angles. Here, angle A₁ matches the acute angle at B, and (of course) angle C matches itself. So, we can name the triangles using those two angles in that order.

  ΔA₁CA ~ ΔBCB₁

3/4 ÷ 3/4

step-by-step explanation:

basically divide any proper fraction with itself to fit the criteria.

so if we are using 3/4, then:

3/4 ÷ 3/4 = 1

so 1 is the quotient.

and the numerators for both these fractions is 3.   and if we divide the numerators:

3 ÷ 3 = 1

we see that quotient is equal to our original quotient as well.