Question

in the figure p is a point on the bisector of angle ABC PQ and PR are the perpendiculars drawn from P to the sides of the angle what is the measure of PQB are the measures of BPQ and BPR equal? why? prove the length of PQ and PR are equal​

Answer 1

Answer:

∠PQB = 90°

Step-by-step explanation:

As given, P is a point of the bisector of ∠ABC,    hence

        ∠RBP = ∠PBQ              ...(1)

(i) As given, PQ is ⊥ drawn on BC,  it means

     PQ makes an angle of 90° with BC

       ∴ ∠PQB = 90°

Similarly,  PR ⊥ BA,   hence ∠PRB = 90°  

In the ΔBPQ & ΔBPR

             BP = BP       (common)

        ∠RBP = ∠PBQ    (from (1))

        ∠PQB = ∠PRB     (from above)

It means, both the triangles are congruent to each other, hence,

   ∠BPQ = ∠BPR       (yes, they are equal)

Similarly, PQ = PR      prove