Similarity of Triangles by AA Criteria


 
 
Concept Explanation
 

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}

Sample Questions
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Question : 1

In the following figure, CB || DE. Find the length of AE.

Right Option : A
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Explanation
Question : 2

The above two triangles are similar by ________________ criteria.

Right Option : C
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Explanation
Question : 3

If in the above figure, angle A=angle D and angle B=angle E .Then the above triangles are similar by ___________________ criteria.

Right Option : B
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Explanation
 
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