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,

`(AN)/(MP)=1,~(AD)/(PR)=(4)/(5).`

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

(9) Here,

`(PS)/(RS)=(SQ)/(ST)=(PR)/(QT)=(2)/(3).`

So, the triangles are similar by proportionality rule.

(10) Here,

`(RQ)/(JK)=(11)/(16),~(PR)/(KL)=(30)/(45)=(2)/(3),~(PQ)/(JL)=(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,

`(GH)/(AC)=(GK)/(AB)=(KH)/(BC)=(1)/(2).`

So, the triangles are similar by the proportionality rule.

Hence explained.