Question

Given: △ABC with a2 + b2 = c2 and right △DEF constructed with legs a and b and hypotenuse n Prove: △ABC is a right triangle. Complete the missing parts of the paragraph proof. Proof: We are given a2 + b2 = c2 for △ABC and right △DEF constructed with legs a and b and hypotenuse n. Since △DEF is a right triangle, we know that a2 + b2 = n2 because of the . By substitution, c2 = n2 Using the square root property and the principle root, we can take the square root of both sides to get c = n. By , triangles ABC and DEF are congruent. Since it is given that ∠F is a right angle, then ∠ is also a right angle by CPCTC. Therefore, △ABC is a right triangle by .

Answer 1

कृपया इस प्रकार के प्रश्न मैथ के विषय में पूछे ।

आपके प्रश्न का उत्तर चित्र में दिया गया है ।

Answer 2

Below is given the total solution.

Explanation:

Given:

           ⇒  $a^{2} +b^{2} =c^{2}$

           ⇒ DE = hypotenuse 'h' with EF = a and DF = b

So, according to question,

                 ⇒ $a^{2} +b^{2} =h^{2}$  

So,

                ⇒ $c^{2} =h^{2}$

                ⇒ c = h

So, by side-side-side property both the triangles are congruent with ∠F as a right angle in second triangle. And, ∠C is the right angle of triangle △ABC due to these lettres are in same side of the notation.