Solve this question with brief diagram and full explanation
Answers
Answer:
Option B is correct
b) △CBA ≅ △PRQ
Answer:
△CBA ≅ △PRQ
Step-by-step explanation:
We have,
AB = QR
BC = PR
CA = PQ
We can solve this in two ways,
Method 1 (Visualization)
Let's draw △ABC (please refer the above image)
Now let's make another similar triangle and begin naming it.
Now, we know that,
AB = QR
BC = PR
CA = PQ
Then, in the corresponding triangle let's mark accordingly, that is, For the side AB let's mark QR, and then mark the 3rd point as P
Now, compare if what we are given is correct, most of the time it will be correct, but we shouldn't lose any mark right,
So, from our image above we see that,
AB = QR
AC = QP
BC = RP
Thus, they are equal.
It doesn't matter if BC is CB because both gives the same magnitude.
Now is the important part,
We have,
△ABC
Now, from our diagram
We take the top A, then left B and then right C
And so we get △ABC
Let's do the same for our similar triangle.
Q is on top, R on left and P on right
So,
Triangle = △QRP
Hence, we get,
△ABC ≅ △QRP
Now don't get confused when the order of both is different because △ABC is the same as △CBA when △QRP is △PRQ, it is just in the reverse order, that will not change the similar sides
Hence,
△CBA ≅ △PRQ
Method 2 (Short trick)
We have,
AB = QR
BC = PR
CA = PQ
Hence, when we compare the congruences we check for the similarities.
Here
1st option is △ABC ≅ △PQR
Here when we compare
AB = PQ
BC = QR
AC = PR
Don't worry about the order
Here we see that it is completely different from what we are given, so it is wrong.
2nd option is △CBA ≅ △PRQ
Comparing,
CB = PR
BA = QR
CA = PQ
Even though the order is different it is exactly what we were given that is
AB = QR
BC = PR
CA = PQ
Hence, option 2 is correct
Let's just refer option 3 also
3rd option is △BAC ≅ △RPQ
Comparing,
BA = RP
AC = PQ
BC = RQ
Again it is not equal to what is given to us.
So, it is wrong.
Hope it helped you and believing you understood it...All the best
