State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement. QRS ~ _

a. similar, SAS, QLK
b. similar, AA, LQK
c. not similar
d. similar, SSS, LQK​

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In ΔQRS and ΔQLK,

QR/QL = QS/QK

28/4 = 28/4

7/1 = 7/1 --[1]

AngleLQK and AngleRQS are equal (VOA)

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

[A] ΔQRS ~ ΔQLK by SAS similarity.

. similar, AAA QLK

Step-by-step explanation:

<K=<L base angle of isosceles triangle

<R=<S base angle of isosceles triangle

<KQL=<RQS vertically opposite angle

so

<K=<L=<R=<S

so

∆QRS~QLK by AAA axiom

step-by-step explanation:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .