Question

In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see figure). Show that ∆ABC ≅ ∆ABD. What can you say about BC and BD?​

Answer 1

Question :-

In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see figure). Show that ∆ABC ≅ ∆ABD. What can you say about BC and BD

Given :-

• AC = AD
• AB bisects Angle A

To prove :-

• ∆ABC ≅ ∆ABD

proof :-

$\longrightarrow \sf \: in \: \triangle \: abc \: and \: \triangle \: abd \: \\ \\ \longrightarrow \sf \: ab \: = ab \: (common) \\ \\ \longrightarrow \sf \: \angle \: cab = \angle \: dab (from2) \\ \\ \longrightarrow \sf \: ac = ad(from1) \\ \\ \longrightarrow \sf \therefore \: \triangle \: abc \: = abd \: (sas) \\ \\ \longrightarrow \sf \therefore \: bc \: = bd \: (cpct)$

therefore BC and BD are of equal length

Answer 2

Follow the steps given by the above person.

At last conclude this sentence:-

By SAS criteria

It is proved that ∆ABC ≅ ∆ABD, Hence by Corresponding Parts of Congruent Triangle are same (CPCT) ,BC = BD