Question

triangle abc bisectors of angle b and angle c meet at p through p a line lm is drawn parallel to bc meeting ab at l and ac at l and ac at m show that lm = bl + cm​

Answer 1

Answer:

Step-by-step explanation:

Given: In ΔABC,

Line LM ║ Line BC

Ray BP is the bisector of ∠ABC

Ray CP is the bisector of ∠ACB

To prove: LM=LB+CM

Proof: ∠LBP ≅ ∠PBC......1...( Ray BP is bisector )

Line LM║ Line BC and Ray BP is transversal

∴ ∠LPB ≅ ∠PBC......2...(Alternate angles )

∴ ∠LBP ≅ ∠LPB........From 1 and 2

∴ Side LB ║ Side LP.......3..( Isoceles triangle theorem)

∠MPC ≅ ∠PCB........4......(Ray CP is bisector)

Line LM ║ line BC and ray CP is transversal

∠MPC ≅ ∠PCB........5.....( alternate angles )

∴ ∠MCP ≅ ∠MPC........From 4 and 5

∴ Side MP≅ side CM......6....(Isoceles triangle theorem)

Now,

LM = LP + PM.........(L-P-M)

∴ From 3 and 6

LM = LB + CM

Hence proved, LM = LB + CM

Answer 2

Answer:

Answer is in Cleary explained in image

Hope it is helpful