We measure the apparent shapes for a sample of 62 blue compact dwarf galaxies ( BCDs ) , and compare them with the apparent shapes for a sample of 80 dwarf elliptical galaxies ( dEs ) .
The BCDs are flatter , on average , than the dEs , but the difference is only marginally significant .
We then use both non-parametric and parametric techniques to determine possible distributions of intrinsic shapes for the BCDs .
The hypothesis that BCDs are oblate spheroids can be ruled out with a high confidence level ( > 99 \% ) , but the hypothesis that they are prolate spheroids can not be excluded .
The apparent shapes of BCDs are totally consistent with the hypothesis that they are triaxial ellipsoids .
If the intrinsic axis ratios , \beta and \gamma , are distributed according to a Gaussian with means \beta _ { 0 } and \gamma _ { 0 } and standard deviation \sigma , we find the best-fitting distribution for BCDs has ( \beta _ { 0 } , \gamma _ { 0 } , \sigma ) = ( 0.66 , 0.55 , 0.16 ) , while that for dEs has ( \beta _ { 0 } , \gamma _ { 0 } , \sigma ) = ( 0.85 , 0.64 , 0.24 ) .
Our results are consistent with the hypothesis that BCDs have a close evolutionary relation with dEs .