Please answer correctly and fast
Answers
Answer:
according to ASA congruency
Step-by-step explanation:
Tri ABC and Tri ADE are congruent to each other.
hence BC=DE
In the given figure,
AC = AE
AB = AD
∠BAD = ∠CAE
Prove that, BC = DE
To Prove :-
BC = DE
Given that,
∠BAD = ∠CAE
On adding ∠DAC on both sides,
∠BAD + ∠DAC = ∠CAE + ∠DAC
⟹ ∠BAC = ∠DAE
Now, Consider
Therefore,
Hence,
Additional Information :
1) AAS Congruency :
If two angles and one side of one triangle is equal to two angles and one side of a triangle, then they are congruent.
Example :
In ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E and BC= EF then ΔABC ≅ ΔDEF by AAS criteria.
2) ASA Congruency :
If two angles and included side of one triangle are respectively equal to two angles and included side of another triangle, then the two triangles are congruent.
Example :
In ΔABC and ΔDEF, ∠A = ∠D, ∠C = ∠F and AC = DF then ΔABC ≅ ΔDEF by ASA criteria.
3) SSS Congruency :
If the corresponding sides of two triangles are equall, then the two triangles are congruent.
Example :
In ΔXYZ and ΔLMN, XY = LM, YZ = MN and XZ = LN then ΔXYZ ≅ ΔLMN by SSS criteria.
4) SAS Congruency :
If in two triangles, one pair of corresponding sides are equall and the included angles are equal then the two triangles are congruent.
Example :
In ∆ABC & ∆DEF,∠A = ∠D, AB = DE, AC = DF then ∆ABC ≅ ∆DEF by SAS criteria.
5) RHS Congruency :
If in two triangles, right angle, Hypotenuse and one side are equal, then triangles are congruent.
Example :
In ∆ABC & ∆DEF,∠A = ∠D = 90°, AB = DE, BC = EF then ∆ABC ≅ ∆DEF by RHS criteria.