AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that∠ BAD = ∠ ABE and ∠ EPA = ∠ DPB (see Fig. 7.22). Show that
(i) Δ DAP ≅Δ EBP

(ii) AD = BE

Question

Philoid · Accepted Answer

It is given in the question that:

P is the mid-point of AB

∠BAD = ∠ABE and,

∠EPA = ∠DPB

(i) ∠EPA = ∠DPB (Adding ∠DPE both sides)

∠EPA + ∠DPE = ∠DPB + ∠DPE

∠DPA = ∠EPB

In

∠DPA = ∠EPB

AP = BP (P is the mid-point of AB)

∠BAD = ∠ABE (Given)

Therefore,

By ASA congruence,

(ii) AD = BE (By c.p.c.t)

AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that∠ BAD = ∠ ABE and ∠ EPA = ∠ DPB (see Fig. 7.22). Show that(i) Δ DAP ≅Δ EBP(ii) AD = BE