In the right △abc, cd is the altitude to the hypotenuse ab and m∠abc=30°. find ad, if bd=54 cm.

The ratios of sides in a 30°-60°-90° triangle are such that the hypotenuse (AB) is double the length of the shortest side (AC). In your triangle, AC is the hypotenuse of similar triangle ACD, which has AD as its shortest side.

Then

(1/2)×(AD+54) = AC

(1/2)×AC = AD

Together, these tell you

AD = (1/4)(AD +54)

3×AD = 54

AD = 18

∠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.

the expression (1.26)2t reveals the approximate rate of increases in the number of plants semiannually.

hope this : )