Similarity of Triangles by SAS Criteria:
Theorem: If in two triangles one pair of corresponding sides are proportional and the included angles are equal then the two triangles are similar.
Given in ABC and DEF and To Prove Construction: Cut DX equal to AB and DY equal to AC. Join XY Proof: It has been given
Replacing Ab with DX and AC with DY
Taking Reciprocal and subtracting 1 from both sides [ Converse of basic proportionality theorem ] [Corresponding angles] .......................(1) AB = DX [By Construction ] AC = DY [By Construction ] [Given] ........................(2) From Eq (1) and (2)
Therefore [By AAA Similarity Criterion] |
Illustration: If AD and PM are medians of triangles ABC and PQR respectively where Prove that | |
Solution: Given .............................(1) As AD and PM are the medians so
BC= 2BD=2CD and QR= 2 QM= 2MR ......................(2) From Eq 1 ......................(3) [From Equation (3) [Proved Above] [By SAS Similarity Criterion ] Thus Hence Proved |
Check whether the two triangles are similar or not. If so, write the similarity relation. | |||
Right Option : C | |||
View Explanation |
If then the above triangles are similar by ________________ criteria. | |||
Right Option : C | |||
View Explanation |
Find the value of x if the triangles are similar by SAS criteria. | |||
Right Option : C | |||
View Explanation |
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