Final answer:
The Grimké sisters became involved in the women's rights movement after joining the abolitionist movement and experiencing resistance to their public advocacy, which included giving lectures to mixed-gender audiences.
Step-by-step explanation:
The sisters Angelina and Sarah Grimké became involved in the women's rights movement after joining the movement to abolish slavery. Initially, they were part of the abolitionist sentiment prevalent in the North, having migrated from the South and converted to Quakerism due to their anti-slavery position. In the mid-1830s, the Grimké sisters embarked on public lecture tours, advocating for immediate abolition to audiences that included both women and men, leading to scandal and further opposition. Their experiences not only with the resistance to their abolitionist voices but also to their breaking of gender norms in their lecture tours, led them to draw parallels between the oppression of slaves and the condition of women, thus propelling their activism into the realm of women's rights as well as abolition.