Question

"A student made the following chart to prove that AB2 + BC2 = AC2.

Answer 1

Step two is incorrect

Answer 2

Solution:

Given : In triangle ABC right angled at B.

To Prove : $AB^2 + BC^2= AC^2$

Construction: Draw B D perpendicular AC.

Proof: 1. Triangle ABC is similar to triangle BDC 1. Angle ABC = Angle BDC and Angle BCA = Angle BCD  

2.$BC^2$ = AC × DC 2. BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC  

3. Triangle ABC is similar to triangle ABD 3. Angle ABC = Angle BAD and Angle BAC = Angle ABD  

4. $AB^2$  = AC × AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ABD  

5.$AB^2 + BC^2 = AC \times AD + AC \times DC$

= AC (AD + DC)  

6. Adding Statement 1 and Statement 2  

7. $AB^2 + BC^2= AC^2$

→→→Statement 3 is incorrect.It should be replaced by, Angle ABC = Angle ADB and Angle B AC = Angle BAD .