Question

Prove that ABC is a right triangle. Select the correct answer from each drop down menu.

Answer 1

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.

To know more about Right Angled Triangle

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