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SAS Similarity : If in two triangles, one pair of corresponding sides are proportional and the included angles are equal then the two triangles are similar. AB AC  =  DE DF 


1) AB = DP ; ∠A = ∠D and AC = DQ  1) Given and by construction 
2) ΔABC ≅ ΔDPQ  2) By SAS postulate 
3) AB AC  =  DE DF 
3) Given 
4) DP DQ  =  DE DF 
4) By substitution 
5) PQ  EF  5) By converse of basic proportionality theorem 
6) ∠DPQ = ∠E and ∠DQP = ∠F  6) Corresponding angles 
7) ΔDPQ ~ ΔDEF  7) By AAA similarity 
8) ΔABC ~ ΔDEF  8) From (2) and (7) 


1) QT / PR = QR / QS  1) Given 
2) QT / QR = PR / QS  2) By alternendo 
3) ∠1 = ∠2  3) Given 
4) PR = PQ  4) Side opposite to equal angles are equal. 
5) QT / QR = PQ / QS  5) By substitution from (2) 
6) PQ / QT = QS / QR  6) By alternendo 
7) ∠PQS = ∠TQR  7) Reflexive (common) in Δ PQS and ΔTQR 
8) ΔPQS ~ Δ TQR  8) By SAS postulate 
RussiaUkraine crisis update  3rd Mar 2022
The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.