Hypotenuse Leg Criteria

Hypotenuse-Leg triangle congruence criteria can be proved similarly to how SSS was proved. An auxiliary line is drawn from B to E, which creates an isosceles triangle, BAE (blue triangle). Why do we know that triangle BCE (orange triangle) is also an isosceles triangle, even though we are not given that BC = EF?

Auxiliary line BE which creates two isosceles triangles, BAE and BCE. Since isosceles triangles have base angles and two sides that are congruent, select all of the relationships below that are true.

Once the following congruent relationships are established, which triangle congruence criteria can be used to establish Hypotenuse Leg criteria?

• AC = DF
• AB = DE
• BC = EF
• angle ABC = angle DEF since all right angles are congruent