Congruence of Triangles By AAS Criteria
Congruence of Triangles by AAS Criteria
Theorem : If any two angles and a non-included side of one triangle are equal to the corresponding angles and side of another triangle, then the two triangles are congruent.
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Given: Two To Prove: Proof: We have, Similarly,
Arrange the terms, we have
Thus, in Now, in BC = EF [Given] and, So, by ASA criterion of congruence, Hence Proved |
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Theorem: If two angles of a triangle are equal. then sides opposite to them are also equal.
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Given: A To Prove: AB = AC Construction: Draw the bisector of Proof: In So, by AAS criterion of congruence, we have
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Illustration: If is an isosceles triangle with AB = AC. Prove that the perpendiculars from the vertices B and C to their opposite sides are equal.
Solution: In , we have
AB = AC [Given]
..........................(i) [
Angles opposite to equal sides are equal]
Now, in , we have
[From (i)]
[Each equal to
]
and, BD = BC [Common]
So, by AAS criterion of congruence, we have
[
Corresponding parts of congruent triangles are equal]
Hence, BD = CE
In the following figure, If
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| Right Option : C | |||
| View Explanation |
If the two triangles are congruent by AAS criteria. | |||
| Right Option : B | |||
| View Explanation | |||
In figure given below, AD is a median and BL, CM are perpendiculars drawn from B and C respectively on AD and AD produced. Then | |||
| Right Option : D | |||
| View Explanation |
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