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 with explanation:

In Δ L V U and Δ G OE

⇒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.

45

step-by-step explanation:

30+15

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!