Question

ਪ੍ਰ:- 5. In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are: ਤ੍ਰਿਭੁਜਾਂ ABC ਅਤੇ PQR ਵਿੱਚ, AB = AC, ∠C = ∠P ਅਤੇ ∠B = ∠Q ਹੋਵੇ ਤਾਂ ਦਿੱਤੇ ਗਏ ਤ੍ਰਿਭੁਜ: यदि त्रिभुज ABC और PQR में AB = AC, ∠C = ∠P और ∠B = ∠Q है तो दिए गए त्रिभुज: *

Isosceles but not congruent / ਸਮਦੋਭੁਜੀ ਪਰ ਸਰਬੰਗਸਮ ਨਹੀਂ / समद्विबाहु हैं पर सर्वांगसम नहीं।

Isosceles and congruent / ਸਮਦੋਭੁਜੀ ਅਤੇ ਸਰਬੰਗਸਮ / समद्विबाहु और सर्वांगसम है।

Congruent but not isosceles / ਸਰਬੰਗਸਮ ਪਰ ਸਮਦੋਭੁਜੀ ਨਹੀਂ / सर्वांगसम हैं पर समद्विबाहु नहीं।

Neither congruent nor isosceles / ਨਾ ਸਰਬੰਗਸਮ ਤੇ ਨਾ ਹੀ ਸਮਦੋਭੁਜੀ / न सर्वांगसम हैं और न ही समद्विबाहु।

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Answer 1

Given :- In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are:

A) Isosceles but not congruent.

B) Isosceles and congruent .

C) Congruent but not isosceles .

D) Neither congruent nor isosceles .

Solution :-

in ∆ABC, we have,

→ AB = AC

So,

→ ∠B = ∠C { when two sides of triangle are equal than there opposite angles are also equal. }

given now,

• ∠B = ∠Q
• ∠C = ∠P

then,

→ ∠P = ∠Q

So,

→ PR = QR. { sides opposite to equal angles are equal. }

Therefore, ∆PQR is also an Isosceles ∆ .

Now, In ∆ABC and ∆PQR , we have,

→ ∠B = ∠Q ( Given)

→ ∠C = ∠P (Given)

So,

→ ∆ABC ~ ∆PQR (By AA similarity.)

Therefore, both triangles are Isosceles but not congruent . (Option A) .

{ Because the triangles can have the same angles but be different sizes . Without knowing at least one side, we can't be sure if two triangles are congruent. }

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3.

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Answer 2

$\large\bf{\underline\green{☕︎Good \: Morning☕︎}}$

In △ABC and △PQR

∠C=∠P (Given)

∠B=∠Q (Given)

∠A=∠R (Third angle of the triangle)

Thus, △ABC∼△PQR

Also, given, AB=AC

Thus, ∠B=∠C (Isosceles triangle Property)

But, ∠B=∠Q and ∠C=∠P

Hence, ∠Q=∠P

or PR=QR

Thus, both the triangles are Isosceles but not congruent.

options A is correct.