Question

Triangle ABC is an isosceles triangle in which AB=AC. side BA is produced to D such that AD=AB. Show that angle BCD is a right angle​

Answer 1

Answer:

∠BCD=90°

Hence, it is proved

See below for detail explanation.

Step-by-step explanation:

In triangle ABC, AB=AC ( given)

                          BA produced to D such that AD=AB

 To proof : ∠BCD=90°

  Solution: In triangle ABC

AB=AC  

∠ABC=∠ACB= y°

∠DAB= 180° ( straight angle)

also, ∠DAC=∠BAC= 90°  (AB=AD)

∠BAC+∠ABC+∠ACB= 180

90° +y+y=180°

2y=90

y=45°

  In triangle ADC,

AB=AC and AB=AD ( given)

According to above,

AC=AD

∠ACD=∠ADC=x

So, ∠CAD+∠ACD+∠ADC= 180°

90°+x+x= 180°

90°+2x=180°

2x=90°

x=45°

x+y⇒45+45=90°

∠ACD+∠ACB= 90°

∠BCD=90°

Hence, it is proved