the aorta is the large artery leaving the heart branches into smaller arteries, which eventually branch into capillaries.the arteries carry oxygen and nutrients away from your heart, to your body's tissues. the capillaries are small, thin blood vessels that connect the arteries and the veins. the statement that arteries carry oxygen-rich blood to capillaries is true. veins on the other hand are blood vessels that take oxygen-poor blood back to the heart.