Question

Determine whether the triangles are similar. if so, write a similarity statement and name the postulate ot theorem you used. if not, explain​

Answer 1

Answer:  Explained.

Step-by-step explanation:  The explanations are as follows :

(7) Since GF is parallel to JK and FK and GJ are tranversals, so we have

∠GFK = ∠JKH,

∠FGK = ∠KJH (pairs of alternate interior angles) and

∠GKF = ∠JHK (vertically opposite angles).

Therefore, both the triangles are similar by AAA similarity rule.

(8) Here,

$\dfrac{AN}{MP}=1,~\dfrac{AD}{PR}=\dfrac{4}{5}.$

Since the ratio of the corresponding sides are not proportional, so the triangles are not similar.

(9) Here,

$\dfrac{PS}{RS}=\dfrac{SQ}{ST}=\dfrac{PR}{QT}=\dfrac{2}{3}.$

So, the triangles are similar by proportionality rule.

(10) Here,

$\dfrac{RQ}{JK}=\dfrac{11}{16},~\dfrac{PR}{KL}=\dfrac{30}{45}=\dfrac{2}{3},~\dfrac{PQ}{JL}=\dfrac{2}{3}.$

Since all the ratios are not equal, so the triangles are not similar.

(11) Here , no angle of one triangle matches with the angle of the other triangle, so the given triangles are not similar.

(12) Here,

$\dfrac{GH}{AC}=\dfrac{GK}{AB}=\dfrac{KH}{BC}=\dfrac{1}{2}.$

So, the triangles are similar by the proportionality rule.

Hence explained.