XYZ is the midsegment of PQR. Enter a congruence statement involving all four of the smaller triangles. What is the relationship between the area of XYZ and PQR? QXY ? XPZ ? YZR ? ZYX

The area of XYZ is 1/? of the area of PQR

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

answer: correct

step-by-step explanation: