Question

in figure, BP is bisector of triangle ABC, SQ perpendicular AB and SR perpendicular BC . prove QS is equall SR ​

Answer 1

Answer:

• BP bisects ∠ABC  ⇒  BS bisects ∠QBR  ⇒  ∠SBQ = ∠SBR
• SQ⊥AB and SR⊥BC  ⇒  ∠SQB = ∠SRB

⇒  Triangles SBQ and SBR are similar since their angles are equal (AA).

• SB is a common side

⇒  Triangles SBQ and SBR are congruent (AAS)

Therefore QS = RS.

Answer 2

Step-by-step explanation:

Given: L Q = L R

L ABP = L PBR (BP is the bisector of L ABC)

BP = BP ( Common side)

Hence, Triangle QBS congruent to Triangle RBS

( By AAS rule)

Hence, QS=SR (CPCT rule)

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