Question

In the figure given below, which of the pairs of triangles are congruent?(Assume that DE and FG are perpendicular bisectors of AX and AY respectively)

• A. $△$ ABX and $△$ ACY
• B. $△$ ACR and $△$ YCR
• C. $△$ ABC and $△$ ACR
• D. $△$ ABQ and $△$ XBQ

Answer 1

Answer: (B), (D)

The correct options are
B $△$ ACR and $△$ YCR
D $△$ ABQ and $△$ XBQ

There are 2 pairs of congruent triangles in the given figure.

If we take $△$ XBQ and $△$ ABQ, we have

XQ = AQ (perpendicular bisector)

$\angle$ BQX = $\angle$ AQB = ${90}^{\circ }$ (perpendicular bisector)

BQ = BQ (common side)

$△$ XBQ $\cong$ $△$ ABQ (By SAS Congruency)

Similarly, taking $△$ ACR and $△$ YCR, we have

AR = YR (perpendicular bisector)

$\angle$ ARC = $\angle$ YRC = ${90}^{\circ }$ (perpendicular bisector)

CR = CR (common side)

$△$ ACR $\cong$ $△$ YCR (By SAS Congruency)