Question

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. The diagram is not drawn to scale.

Answer 1

Answer:

Givn : OK = 3, OJ = 30, KN = 1, JM = 3

ON=OK+KN=3+1=4

OM=OJ+JM=30+10=40

In triangles OKJ & ONM,

OKOJ=330=110

ONOM=440=110

Angle O is common in both the triangles.

Two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.

That means KJNM=110 or the two sides are parallel.

Hence ˆK=ˆN,ˆJ=ˆM corresponding angles.

Answer 2

Givn : OK = 3, OJ = 30, KN = 1, JM = 3

ON=OK+KN=3+1=4

OM=OJ+JM=30+10=40

In triangles OKJ & ONM,

OKOJ=330=110

ONOM=440=110

Angle O is common in both the triangles.

Two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.

That means KJNM=110 or the two sides are parallel.

Hence ˆK=ˆN,ˆJ=ˆM corresponding angles.