All the blanks have been filled , which proves ultimately that Triangle ABC is a right angled Triangle.
What is Right Angled Triangle ?
A triangle in which one angle is 90 degree is called a Right Angled Triangle.
AB is congruent to DB because segment DE was constructed so that DE = AB , BC is congruent to EF , because segment EF was constructed so that EF = BC , Since Triangle DEF is a right angled triangle .
DE² +EF² = DF² by the Pythagoras Theorem .
WE are given that AB² +BC² = AC²
Since DE = AB and EF = BC , DE² +EF² = AC² by the given data
Also DF² = AC² by the above equation .
Taking the square root on both the sides of the equation gives DF = AC .
So AC is congruent to DF by the definition of congruency .
Applying SSS Congruency , Triangle ABC is congruent to DEF .Therefore ABC is a right angled triangle.
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