Question

21. In the given figure, ZCPD = ZBPD and AD bisects ZBAC. Show that AACP AABP and hence CP = BP. (Hint: ZCPA = ZBPA)​

Answer 1

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(i) ⟨DAC = ⟨BAC

→ ⟨DCA = ⟨BCA

→ AC = AC

(ii) By ASA criterion, triangles are congruent.

(iii) Since triangles are congruent hence, AB=AD because both sides originate from equal angles in two triangles.

(iv) Since triangles are congruent hence,CD=CB because both sides originate from equal angles in two triangles.

Answer 2

(i) ⟨DAC = ⟨BAC

→ ⟨DCA = ⟨BCA

→ AC = AC

(ii) By ASA criterion, triangles are congruent.

(iii) Since triangles are congruent hence, AB=AD because both sides originate from equal angles in two triangles.

(iv) Since triangles are congruent hence,CD=CB because both sides originate from equal angles in two triangles.