Congruence of Triangles By SAS Criteria
Congruence of Triangles By SAS Criteria
Theorem: Two triangles are congruent if two sides and the included angle of one are equal to the corresponding sides and the included angle of the other triangle.
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Given: Two triangles ABC and DEF such that To Prove: Proof: Place As AB = DE [Given] So vertex B falls on vertex E. Since But AC = DF [ Given] Therefore, C will fall on F. Thus, AC coincides with DF. Now, B falls on E and C falls on F. Therefore, BC coincides with EF. Thus, Hence, by definition of congruence, |
| Illustration: In |
 |
Solution: We have,
[
Similarly,
]
.....(i)
In and
we have
AB = PQ [Given]
[From (i)]
and, BC = QR [Given]
So, by SAS criterion of congruence, we have
Illustration: In the given figure, AC = AE, AB = AD and .Show that BC = DE
Solution: We have,
[Given]
[Adding
to both sides]
Now, in triangles ABC and ADE,
[Given]
[From (i)]
and, [Given]
So, by SAS congruence criterion, we have
[CPCT]
In congruent triangles ABC and DEF, ∠A = ∠E = 40∘, and ∠F = 65∘, then ∠B = | |||
| Right Option : C | |||
| View Explanation | |||
In the given figure, AB = AC. If
| |||
| Right Option : B | |||
| View Explanation | |||
In the figure shown above, if the two triangles are congruent by SAS criteria then which of the following conditions are not true? | |||
| Right Option : C | |||
| View Explanation | |||
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