Please help ASAP!! Thank you

This is so hard and it’s for a test

In a right triangle δabc, the length of leg ac = 5 ft and the hypotenuse ab = 13 ft. find: b the length of the angle bisector of angle ∠a.

Examine the paragraph proof. which theorem does it offer proof for? prove jnm – nmi according to the given information in the image. jk | hi while jnm and lnk are vertical angles. jnm and lnk are congruent by the vertical angles theorem. because lnk and nmi are corresponding angles, they are congruent according to the corresponding angles theorem. finally, jnm is congruent to nmi by the transitive property of equality alternate interior angles theorem gorresponding angle theorem vertical angle theorem o same side interior angles theorem