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. $△ABC\&△AMC$
• B. $△ABC\&△ADC$
• C. $△ABC\&△AMD$
• D. $△AMC\&△AMD$

Answer 1

The correct option is D $△AMC\&△AMD$

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° (perpendicular bisector) ​

AM = AM (common side) ​

$△$AMC ≅ $△$AMD (By SAS Congruency) ​

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Answer: (D) $△$ AMC and $△$ AMD