By the Hypotenuse Leg theorem, the two triangles are congruent. That is, ΔBXA ≅ ΔBYA
From the question, we are to prove that ΔBXA ≅ ΔBYA
From the Hypotenuse Leg theorem which states that "two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side".
From the given information,
BX ⊥ XA.
ΔBXA is right triangle with hypotenuse AB
Also,
BY ⊥ YA.
ΔBYA is right triangle with hypotenuse AB
∴ The hypotenuses of the triangles are congruent
Also, from the given information,
XA is congruent to YA
XA and YA are the legs of the right triangles.
Hence, by the Hypotenuse Leg theorem, the two triangles are congruent. That is, ΔBXA ≅ ΔBYA
Learn more on Congruent triangles here: brainly.com/question/27983954
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