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Course / Category - 10th NTSE

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NTSE

10th NTSE

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Maths / Triangles / Similarity of Triangles by AA Criteria

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Similarity of Triangles by AA Criteria

Similarity of Triangles by AA criteria:

Corollary If two angles of a triangle are respectively equal to two angles of another triangle, then two triangles are similar.

Given In $large Delta ABC ; and; Delta DEF$

$large angle A=angle D,; and;angle B=angle E$

To Prove : $large Delta ABCsim Delta DEF$

Proof: As in $large Delta ABC ; and; Delta DEF$

$large angle A=angle D,; and;angle B=angle E$

From Angle Sum Property we can prove that if two angles of one triangle is equal to two angles of other triangle

Therefore $large angle C=angle F$

Then from the theorem of AAA Similarity criterion we can say that

$large Delta ABCsim Delta DEF$

Hence Proved

Illustration : ABC and AMP are two right triangles right angled at B and M repectively. Prove that

$large (1);; Delta ABCsimDelta AMP$

$large (2);; frac{CA}{PA}= frac{BC}{MP}$

Solution: In $large In; Delta ABC; and;Delta AMP$

$large angle A=angle A$ [Common]

$large angle B=angle M$ [Each Right Angle]

Therefore $large Delta ABCsimDelta AMP$ [ AA Similarily Criterion]

$large frac{AB}{AM}=frac{AC}{AP} = frac{BC}{MP}$

Hence $large frac{CA}{PA}= frac{BC}{MP}$

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Similarity of Triangles by AA Criteria

₹17200 ₹12000 +
Taxes