Given below are some of the measures of the sides and angles of five triangles. Which of the triangles given in the options is NOT congruent to triangle ABC ?
In ΔABC, m\(\overline{(AB)}\) = 3.6 cm, m\(\overline{(BC)}\) = 5 cm, m\(\overline{(CA)}\) = 4 cm, m (∠B) = 52.4o, m(∠C) = 45.5o
In ΔDEF, m\(\overline{(DE)}\) = 4 cm, m\(\overline{(EF)}\) = 5 cm, m\(\overline{(FD)}\) = 3.6 cm
In ΔGHI, m\(\overline{(HI)}\) = 5 cm, m(∠H) = 52.4o, m(∠I) = 45.5o
In ΔJKL, m\(\overline{(JK)}\) = 3.6 cm, m\(\overline{(LJ)}\) = 4 cm, m(∠J) = 52.4o
In ΔMNO, m\(\overline{(MN)}\) = 3.6 cm, m\(\overline{(NO)}\) = 5 cm, m(∠N) = 52.4o
Answer & explanation
Correct answer: option 3
Concept Used
Two triangles are congruent if the corresponding sides are equal and the corresponding angles are equal.
Calculations
Considering JKL, we have
Here we have JK = 3.6 cm, JL = 4 cm \(\angle\)J = \({52.4}^\circ\)
Since, angle included between the two sides of triangle JKL is not equal to the angle included between the two sides of triangle ABC. Hence, triangle JKL does not follow the property of SAS (Side - Angle - Side) So, JKL is not congruent to ABC.