It seems like you inverted Y axis and Z axis in your triangles. You probably wanted to write this:
glTexCoord2f(0,0); glVertex3f(-10, 0, 0);
glTexCoord2f(1,0); glVertex3f(10, 0, 0);
glTexCoord2f(0,1); glVertex3f(-10, 5, 0);
glTexCoord2f(1,1); glVertex3f(10, 5, 0);
This corresponds better to the figure you attached to your question.