Question

Match the column.

1. In $\Delta ABC$ and $\Delta PQR$, $\frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$	(a) AA similarity criterion
2. In $\Delta ABC$ and $\Delta PQR$, $\angle A=\angle P,\angle B=\angle Q$	(b) SAS similarity criterion
3. In $\Delta ABC$ and $\Delta PQR$, $\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$ $\angle A=\angle P$	(c) SSS similarity criterion
4. In $\Delta ACB,DE||BC$ $\Rightarrow \frac{AD}{BD}=\frac{AE}{CE}$	(d) BPT

• A. $1\to a,2\to b,3\to c,4\to d$
• B. $a\to d,2\to a,3\to c,4\to b$
• C. $1\to b,2\to a,3\to c,4\to d$
• D. $1\to c,2\to b,3\to d,4\to a$

Answer 1

The correct option is C $1\to b,2\to a,3\to c,4\to d$

In $△ABC$ and $△PQR$

Option A:

If $\angle A=\angle P$ ....Given

And, $\frac{AB}{PQ}=\frac{AC}{PR}$ ...Given

$△ABC\sim △PQR$ ...SAS test of similarity

Option B:

If $\angle A=\angle P$ ....Given

And $\angle B=\angle Q$ ....Given

$△ABC\sim △PQR$ ...AA test of similarity

Option C:

If $\angle A=\angle P$ ....Given

And $\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$ ....Given

$△ABC\sim △PQR$ ...SS S test of similarity

Option D:

In $△ACB,DE\parallel BC$

$\frac{AD}{BD}=\frac{AE}{CE}$ ....Given

This is known as basic proportionality theorem.