Question

Determine whether each pair of triangles is similar. If similarity exists, write a congruency statement relating to the two triangles. Give a justification for your answer.

Answer 1

To be similar ratios of the corresponding sides should be constant.

|UV|/|EO| = 8/4=2/1

|VL|/|OG| = 4/2=2/1

|LU|/|GE| = 6/3 = 2/1

So,all three corresponding pair of these triangles UVL and EOG are in proportion, so ΔUVL and ΔEOG are similar.

Because ΔUVL and ΔEOG are similar, their corresponding angles are congruent.

m∠U=m∠E

m∠V=m∠O

m∠L=m∠G.

Answer 2

Answer with explanation:

In Δ L V U and Δ G OE

$\frac{GO}{LV}(\frac{2}{4})=\frac{OE}{UV}(\frac{4}{8})=\frac{GE}{UL}(\frac{3}{6})=\frac{1}{2}$

⇒Δ L V U ~ Δ G OE-------[Side-Side-Side(SSS)]

If Corresponding sides of Triangle are Proportional, then two triangles are Similar.

By C PCT

→∠L=∠G

→∠V=∠O

→∠U=∠E

Also , if two triangles are Similar, then the Triangles may or may not be Congruent, but if triangles are Congruent then it guarantees similarity of triangles .

⇒Δ L V U and Δ G OE , would have been Congruent, if their corresponding sides would have been equal that is by SSS, S AS,A AS.Here the two triangles are not congruent.