Answer:
- ∠1≅∠2-------------------------(Given)
- m∠1=m∠2-------------------(Definition of congruent angles)
- ∠ABP, ∠1 and ∠DCP,∠2 form linear pair---------------Linear pair
- m∠ABP+m∠1=180° and m∠DCP+m∠2=180°--------definition of linear pair
- ∠ABP≅∠DCP--------------------If equals are subtracted from equals, the remainders are equal
- AP≅DP----------------------------Given
- ΔABP≅ΔDCP-------------------AAS
Step-by-step explanation:
Given, ∠1≅∠2, ∠3≅∠4 and AP≅DP,
∠1≅∠2(given)
⇒m∠1=m∠2(definition of congruent angles)
- ∠[tex]ABP+[/tex]m∠1=180° and ∠[tex]DCP[/tex]+m∠2=180° (Linear Pair)
180°=180°(Reflexive)
⇒m∠[tex]ABP+[/tex]m∠1=m∠[tex]DCP[/tex]+m∠2
But m∠1 =m∠2 (definition of congruent angles)
⇒m∠[tex]ABP+[/tex]m∠1=m∠[tex]DCP[/tex]+m∠1
m∠[tex]ABP+[/tex]=m∠[tex]DCP[/tex] ( If equals are subtracted from equals, the remainders are equal)
- [tex]AP[/tex]=[tex]DP[/tex](GIven)
Therefore, Δ[tex]ABP=[/tex]Δ[tex]DCP[/tex] (by AAS criteria)
condition are:
- m∠1=m∠2 (Angle)
- m∠[tex]ABP[/tex]=m∠[tex]DCP[/tex] (Angle)
- AP=DP (Side)
