Question

During the construction of a triangle given its base, a base angle and the sum of other two sides, which of the triangles formed are congruent?

• A. $△$ ABC and $△$ AMC
• B. $△$ ABC and $△$ ADC
• C. $△$ ABC and $△$ AMD
• D. $△$ AMC and $△$ AMD

Answer 1

The correct option is D $△$ AMC and $△$ AMD

Given,
Construction of a triangle given its base, a base angle and sum of other two sides.

If we take $△$ AMC and $△$ AMD,
DM = MC (perpendicular bisector bisects the line DC)
$\angle$ AMC = $\angle$ AMD = ${90}^{\circ }$ (perpendicular bisector)
AM = AM (common side)

$△$ AMC $\cong$ $△$ AMD (By SAS Congruency)