Question

In the adjoining figure, AB = 5cm,AC = 5cm,BD = 2.5cm and CD = 2.5cm
1) state the three pairs of equal parts in ΔADB and ΔADC
2) Is ΔADB=ΔADC?Give reasons.
3)Is <B = <C?why?

Answer 1

1) AD = AD (common side )
AB = AC (both are 5 cm)
BD = DC ( both are 2.5 cm)

2) Prove congruent
and then their area is also equal

3) yes <B = <C
In triangle ABC
AB = AC
<ABC = <ACB ... (1)
(opposite angles of equal sides are equal)
In triangle BDC
BD = DC
< DBC = <DCB .... (2)
On adding equation 1 and 2 we get
<ABC + <DBC = <ACB + <DCB
<B = <C

Answer 2

Answer:

1) AD = AD

(common side) (both are 5 cm)

AB = AC

BD = DC

(both are 2.5 cm)

2) Prove congruent and then their area is also equal

3) yes <B=<C

In triangle ABC

AB = AC

<ABC = <ACB ... (1)

(opposite angles of equal sides are equal)

In triangle BDC

BD = DC

DBC = <DCB .... (2)

On adding equation 1 and 2 we get <ABC + <DBC = <ACB + <DCB

<B=<C