AB is three-fifths the length of AD and BC is three-fifths the length of DE. With the information given above, determine how triangle ABC can be shown to be similar to triangle ADE.

See explanation

Step-by-step explanation:

Given:

- AB = 3/5 * AD

- BC = 3/5 * DE

Find:

Determine how triangle ABC can be shown to be similar to triangle ADE.

Solution:

- The law of similar triangles states that all 3 angles must be similar:

                                 AB / AD = BC / DE = AC / AE

- Then using the given data we will prove the above ratios to be equal:

                                (3/5)*AD / AD = (3/5) BC/BC = 3/5

- Now we know that angle A is common to both triangles ABC and ADE we have sum of angles:

                                 A + B + C = A + D + E

                                      B + C = D + E

- Since, angles B and D lie on parallel lines, the law of corresponding angle states that B = D. Hence,

                                            E = C

- Hence, angle B = D , E = C and angle A is common to both. Proves that both ABC and ADE are similar triangles.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for