PROVE THE GIVEN TRIANGLES ARE SIMILAR USING AA SIMILARITY THEOREM

Prove that the given triangles are similar using AA theorem :

Example 1 :

Solution :

Given :

DE || BC

To Prove :

∆ADE ~ ∆ABC

Proof :

In ∆ADE and ∆ABC

<ADE  =  <ABC

<AEC  =  <ACB

(corresponding angles are congruent)

So, ∆ADE and ∆ABC are similar.

Example 2 :

Solution :

Given :

DE || BC

To Prove :

∆ADE ~ ∆ABC

Proof :

In ∆ADE and ∆ABC

<ADE  =  <ABC

<AEC  =  <ACB

(corresponding angles are congruent)

So, ∆ADE and ∆ABC are similar.

Example 3  :

Solution :

Given :

DE || AB

To Prove :

∆DEC ~ ∆ABC

Proof :

In ∆DEC and ∆ABC

<DEC  =  <ABC  (90 degree)

<DCE  =  <ACB  (common)

So, ∆DEC and ∆ABC are similar.

Example 4  :

Solution :

Given :

DE || BC

To Prove :

∆ADE ~ ∆ABC

Proof :

In ∆ADE and ∆ABC

<ADE  =  <ABC

<EAD  =  <CAB

So, ∆ADE and ∆ABC are similar.

Example 5  :

Solution :

Given :

AB || DE

To Prove :

∆ABC ~ ∆DEC

Proof :

In ∆ABC and ∆DEC

<ABC  =  <DEC (90 degree)

<ACB  =  <ECD (vertically opposite angles)

So, ∆ABC and ∆DEC are similar.

Hence, it is proved.

Example 6  :

Given :

AB || DE

To Prove :

∆ABC ~ ∆DEC

Proof :

In ∆ABC and ∆DEC

<ABC  =  <DEC  (90 degree)

<DCE  =  <BCA  (vertically opposite angles)

So, ∆ABC and ∆DEC are similar.

Example 7  :

Given :

DE || BC

To Prove :

∆ADE ~ ∆ABC

Proof :

In ∆ADE and ∆ABC

<ADE  =  <ABC

<EAD  =  <CAB

So, ∆ADE and ∆ABC are similar.

Example 8  :

Solution :

Given :

DE || BC

To Prove :

∆ADE ~ ∆ABC

Proof :

In ∆ADE and ∆ABC

<ADE  =  <ABC (90 degree)

<DAE  =  <BAC (common)

So, ∆ADE and ∆ABC are similar.

Example 9  :

Solution :

Given :

DE || AB

To Prove :

∆DEC ~ ∆ABC

Proof :

In ∆DEC and ∆ABC

<DEC  =  <ABC  (90 degree)

<DCE  =  <ABC  (common)

So, ∆DEC and ∆ABC are similar.

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