Option fourth "By the addition property of equality, AC² plus AB² = BC multiplied by DC plus AB² is correct.
What is the Pythagoras theorem?
The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
The figure is missing.
The right-angle triangle is shown in the picture; please refer to the picture.
The missing options are attached; please refer to the picture.
We have a right-angle triangle shown in the picture.
The larger triangle ABC is similar to the smaller triangles as follows.
ΔABC ~ ΔDBA   (By AA similarity)
ΔABC ~ ΔDAC  (By AA similarity)
From the above similarity:
AC² or AB²
[tex]\rm \dfrac{AB}{BD} = \dfrac{BC}{AB}[/tex]
After cross multiplication:
AB² = BC×BD
Now,
[tex]\rm \dfrac{AC}{CD} = \dfrac{BC}{AC}[/tex]
AC² = BC×BD
AB² + AC² =  BC×BD + BC×BD
AB² + AC² =  2BC×BD
Thus, the option fourth "By the addition property of equality, AC² plus AB² = BC multiplied by DC plus AB² is correct.
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