I am reading Feynman's lost lecture. At this point, he asks us to consider points J, K, L and M which subtend equal angles at the sun S. And then he claims that triangles JKS and KLS are similar because the angles are equal, so their areas are proportional to the square of their dimensions, and thus proportional to the square of the distance, and since time is proportional to the area swept by Kepler's first law, so time taken is proportional to the square of the distance. My question is why must the two triangles be similar? Only one angle is the same.

I am reading Feynman's lost lecture. At this point, he asks us to consider points J, K, L and M which subtend equal angles at the sun S. And then he claims that triangles JKS and KLS are similar because the angles are equal, so their areas are proportional to the square of their dimensions, and thus proportional to the square of the distance, and since time is proportional to the area swept by Kepler's first law, so time taken is proportional to the square of the distance. My question is why must the two triangles be similar? Only one angle is the same. https://wucj.lab.westlake.edu.cn/Others/Feynman_lost_lecture.pdf is the link for the lecture, and the page is 157.

I am reading Feynman's lost lecture. At this point, he asks us to consider points J, K, L and M which subtend equal angles at the sun S. And then he claims that triangles JKS and KLS are similar because the angles are equal, so their areas are proportional to the square of their dimensions, and thus proportional to the square of the distance, and since time is proportional to the area swept by Kepler's first law, so time taken is proportional to the square of the distance. My question is why must the two triangles be similar? Only one angle is the same.  

I am reading Feynman's lost lecture. At this point, he asks us to consider points J, K, L and M which subtend equal angles at the sun S. And then he claims that triangles JKS and KLS are similar because the angles are equal, so their areas are proportional to the square of their dimensions, and thus proportional to the square of the distance, and since time is proportional to the area swept by Kepler's first law, so time taken is proportional to the square of the distance. My question is why must the two triangles be similar? Only one angle is the same.