![]() ![]() Statements Reasons 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. ![]() Statements Reasons 1) AB = DP ∠A = ∠D and AC = DQ 1) Given and by construction 2) ΔABC ≅ ΔDPQ 2) By SAS postulate 3) AB ACĭE 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)ġ) In the given figure, if QT / PR = QR / QS and ∠1 = ∠2. The Following Postulate, As Well As The SSS And SAS Similarity Theorems, Will Be Used In Proofs Just As SSS, SAS, ASA, HL, And AAS Were Used To Prove. to two sides of another triangle and their. Theorem 6.5 (SAS Similarity) - If one angle of a triangle is equal to Chapter 6 Class 10 Triangles Serial order wise Theorems Check sibling questions Theorem 6. Given : Two triangles ABC and DEF such that ∠A = ∠D AB ACĬonstruction : Let P and Q be two points on DE and DF respectively such that DP = AB and DQ = AC. The Side-Angle-Side Similarity (SAS ) Theorem states that if two sides of one triangle are. ![]() To prove the above theorem we need to do some constructions. SAS Similarity 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. If the corresponding sides of the two triangles are proportional the triangles must be similar. SAS Similarity If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. ![]()
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