sss criteria similarties prove
Answers
sss criteria means side side side
if all the sides of the triangles are equal , then the triangle will be congruent by sss pro0erty
Answer:
SSS similarity : If the corresponding sides of two triangles are proportional, then the two triangles are similar.
Step-by-step explanation:
Given : Two triangles ABC and DEF such that
AB BC CA
---- = ------ = ------
DE EF FD
Prove that : ΔABC ~ ΔDEF
Construction : Let P and Q be two points on DE and DF respectively such that DP = AB and DQ = AC. Join PQ.
Statements
Reasons
1) AB AC
---- = ------
DE DF 1) Given
2) DP DQ
---- = ------
DE DF 2) As AB = DP and AC = DQ. By substitution
3) PQ || EF 3) By converse of basic proportionality theorem
4) ∠DPQ = ∠E and ∠DQP = ∠F 4) Corresponding angles
5) ΔDPQ ~ ΔDEF 5) By AA similarity
6) DP PQ
---- = ------
DE EF 6) By definition of similar triangles
7) AB PQ
---- = ------
DE EF 7) As DP = AB , by substitution
8) PQ BC
---- = ------
EF EF 8) From (1) (6) and (7)
9) PQ = BC 9) From (8)
10) ΔABC ≅ ΔDPQ 10) By S-S-S postulate
11) ΔABC ~ ΔDEF 11) From (5) and (10)
Examples
Statements
Reasons
1) AB = 4; AC = 2;CB = 6; DE = 2; DF = 1; FE = 3 1) Given
2) AB BC CA
---- = ------ = ------
DE EF FD 2) Property of proportion
3) ΔABC ~ ΔDEF 3) By S-S-S-similarity