Question

8. AABC is an isosceles triangle in which AB=AC.
Side BA is produced to D such that ADEAB
Show that ZBCD is a right angle.
B​

Answer 1

Answer:

Step-by-step explanation:

Given: △ABC is isosceles and AB=AC.  

Also, AD=AB

In ΔABC

AB=AC

By isosceles triangle theorem,

∠ABC=∠ACB  ----(1)

In ΔADC

By isosceles triangle theorem,

AB=AD=AC  (given)

∴∠ADC=∠ACD  -----(2)

In ΔBCD,

∠ABC+∠BCD+∠BDC=180  

       ...Angle sum property

   ⇒(∠ACB+∠ACD)+∠BCD=180 ----From (1) and (2)

   ⇒∠BCD+∠BCD=180                                                    

   ⇒2∠BCD=180  

   ⇒∠BCD=90  

                [hence proved]

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