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?

Answer :-

In quadrilateral ACBD, we have AC = AD and AB being the bisector of ∠A.

Now, In ∆ABC and ∆ABD,

AC = AD (Given)

∠ CAB = ∠ DAB ( AB bisects ∠ CAB)

and AB = AB (Common)

∴ ∆ ABC ≅ ∆ABD (By SAS congruence axiom)

∴ BC = BD (By CPCT)

Plz mrk as brainliest ❤

Answer 2

✯ answer ✯

given →

・AC = AD

・∠ DAB = ∠ CAB ( AB bisects ∠ A)

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i) show that ∆ABC ≅ ∆ABD

➪ in ∆ABC and ∆ABD

・ AD = AC ( given )

・ ∠DAB = ∠CAB ( given )

・ AB = AB ( common )

→ ∆ABC ≅ ∆ABD by SAS congruency rule

hence, proved!

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ii) what can you say about BC and BD ?

➪ since ∆ABC ≅ ∆ABD

→ BC = BD [ by CPCT (congruent parts of congruent triangles) ]

hence, BC and BD are equal