Home
Class 10
MATHS
In that figure, if Delta ABE ~= Delta AC...

In that figure, if `Delta ABE ~= Delta ACD`, show that `Delta ADE ~= Delta ABC`.

Text Solution

Verified by Experts

`Delta ABE~= Delta ACD` (give)
`:. AE= AD" "...(i)` [cpct]
and `AB =AC" "...(ii)` [ cpct]
In `Delta ADE and Delta ABC`, we have
`angle DEA= angle BAC` (common)
and `(AD)/(AB)=(AE)/(AC)" "` [ using (i) and (ii)]
`:. Delta ADE ~ Delta ABC`[ by SAS-similarity]
Promotional Banner

Similar Questions

Explore conceptually related problems

In the given figure, if angle ADE= angle B , show that Delta ADE~ Delta ABC . If AD=3.8 cm, AE=3.6 cm, BE=2.1 cm, and BC =4.2 cm , find DE.

In figure ,D and E are Points on side BC of a Delta ABC such that BD=CE and AD=AE.Show that Delta ABD cong Delta ACE.

In the adjoining figure,E is a point on the median AD of a Delta ABC. Show that ar (Delta ABE)=(Delta ACE)

In the given figure ar (Delta ABC)=" ar "(Delta ADE) . AC is the median of Delta ADE . If ar (ACE) =14 cm^(2)" then ar "(Delta ABC) = ?

In the same figure, Delta ABC and Delta DBC are on the same base BC . If AD is intersects BC at O, prove that (ar(Delta ABC))/(ar (Delta DBC))=(AO)/(DO)

In the adjoining figure, DE || BC . Prove that area (Delta ACD) = " area " (Delta ABE)

If Delta ABC ~ Delta PQR and 4A (Delta ABC) = 25 A (Delta PQR) then AB : PQ = ?

In the given figure,Delta ABC and Delta DBC are on the same base BC.If AD intersects BC at O , prove that (ar(Delta ABC))/(ar(Delta DBC))=(AO)/(DO)