Question

In the adjoining figure, two triangles FGH and QPR are:

• A. Similar using AA criteria
• B. Similar using SAS criteria
• C. Not similar
• D. None of these

Answer 1

The correct option is B

Similar using SAS criteria

In $\Delta$ FGH,

$\angle F={180}^{\circ }-(\angle G+\angle H)\angle F={180}^{\circ }-({20}^{\circ }+{30}^{\circ })\angle F={130}^{\circ }In\Delta FGHand\Delta QPR\angle F=\angle Q\frac{FG}{PQ}=\frac{63}{7}=\frac{9}{1}-----\left(1\right)\frac{FH}{QR}=\frac{45}{5}=\frac{9}{1}----\left(2\right)$

(1) and (2) are equal

Hence, $\Delta FGH\sim \Delta QPR$ by SAS similarity.