Question

In the following picture, two congruent triangles are shown.

Which of the following are the correct ways to represent their congruency? Check all that apply.

• A. $△ABC\cong △PQR$
• B. $△BCA\cong △QRP$
• C. $△ACB\cong △PRQ$
• D. $△BCA\cong △QPR$

Answer 1

Answer: (A), (B), (C)

$△ACB\cong △PRQ$

The given figure is,

The triangles are given to be congruent.

$\underset{–}{\text{Note}}$: Congruent triangles are named by listing their vertices in corresponding orders.

Clearly, from the figure​​​​​​
$\bullet A$ corresponds to $P$
$\bullet B$ corresponds to $Q$
$\bullet C$ corresponds to $R$.

Now, let us check the options one by one if the vertices are listed in corresponding orders.

(a.) $△ABC\cong △PQR$
$\bullet A$ corresponds to $P$
$\bullet B$ corresponds to $Q$
$\bullet C$ corresponds to $R$
Hence, it is a correct way of representation.

(b.) $△BCA\cong △QRP$
$\bullet B$ corresponds to $Q$
$\bullet C$ corresponds to $R$
$\bullet A$ corresponds to $P$
Hence, it is a correct way of representation.

(c.) $△ACB\cong △PRQ$
$\bullet A$ corresponds to $P$
$\bullet C$ corresponds to $R$
$\bullet B$ corresponds to $Q$
Hence, it is a correct way of representation.

(d.) $△BCA\cong △QPR$
$\bullet B$ corresponds to $Q$
$\bullet C$ does not correspond to $P$
$\bullet A$ does not correspond to $R$
Hence, it is not a correct way of representation.

Thus, options (a.), (b.) and (c.) are correct.