Question

ABC is a triangle with angle b is equal to 90 degree and angle P midpoint of AC prove that PB is equal to PA
is equal to half AC

Answer 1

Given: ABC is a right angled triangle.
ABC=90
PBC=PCB=a
To prove: PA=PB
In ABC,
ABC=90 and ACB=a
The sum of all angles of a triangle is 180.
→ ABC+ACB+BAC=180
→90+a+BAC=180
→BAC=180-90-a
→BAC=90-a …(i)
ABP=ABC-PBC
ABP=90-a …(ii)
→BAC=ABP … from (i) and (ii)
In a triangle sides opposite to equal angles are equal.
→ PA = PB
PA is equal to half AC because P is the mid point of AC.