PQRS is a parallelogram and T is the mid point of PQ if ar PTRS=24 cm^2, find the area of PQR

24 sq cm

Step-by-step explanation:

According to theorem of area if parallelogram and triangle, if the triangle and a parallelogram lie between two parallel line and their base is same then, the area of triangle is half of the area of the parallelogram. so here the parallelogram PTRS and the triangle PTR lie between same parallel lines PT and RS and base is also same PT. so area of PTR is 12sq cm. Again, triangles PTR and TRQ lie between same parallel lines PQ and SR and same base PQ. so their area also same that is 12 sq cm. Now, area of PQR = area of PTR + area of TRQ = 12 + 12 sq cm = 24 sq cm.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

answer:

c) the x-coordinate of the center of the circle increases by 3