If angle A is congruent to itself by the Reflexive property, which transformation could be used to prove triangle ABC is similar to triangle ADE by AA similarity postulate? A. Translate triangle ADE so that point D lies on point B to confirm angle D is congruent to angle B.

B. Translate triangle ADE so that point B lies on point E to confirm angle B is congruent to angle E.

C. Dilate triangle ABC from point A by the ratio segment AD over segment AB to confirm segment AD is similar to segment AB

D. Dilate triangle ABC from point A by the ratio segment AE over AC to confirm segment AE is similar to segment AC.

A. Translate triangle ADE so that point D lies on point B to confirm angle D is congruent to angle B.

Step-by-step explanation:

Two triangles are said to be similar if the ratio of their corresponding sides are equal.

The AA Similarity Postulate states that If two angles of one triangle is congruent to two angles of another triangle, then the two triangles are similar.

Translation is the movement of a point up, down, left or right.

Since ∠A = ∠A (reflexive property of congruence)

We have to prove that ∠D = ∠B, by Translating triangle ADE so that point D lies on point B

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week