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PART - 2 CH : 1 Geometric Twins — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSPART - 2 CH : 1 Geometric Twins5 Marks
Question
ABCD is a square. Show that ∆ABC ≅ ∆ADC. Is ∆ABC also congruent to ∆CDA?
Image
Give more examples of two triangles where one triangle is congruent to the other in two different ways, as in the case above. Can you give an example of two triangles where one is congruent to the other in six different ways?
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Answer

To show ∆ABC ≅ ∆ADC (∵ ABCD is a square)
Now, AD = AB
CD = CB
AC = AC (Common side)
So, ∆ABC ≅ ∆ADC (Using SSS criterion)
For ∆ABC to be congruent to ∆CDA
AB = CD
BC = DA
AC = CA
Since ABCD is a square
Hence, ∆ABC is congruent to ∆CDA by side side-side-side condition.
Now, let us take two congruent triangles ∆HEN and ∆BIG.
Image
There are six ways to write a congruence statement for two congruent triangles.
The other five ways are
(i) ∆HNE ≅ ∆BGI
(ii) ∆EHN ≅ ∆IBG
(iii) ∆ENH ≅ ∆IGB
(iv) ∆NHE ≅ ∆GBI
(v) ∆NEH ≅ ∆GIB
(vi) ∆HEN ≅ ∆BEN

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