Question 7 - Congruency - Different Criteria's - Congruence of Triangles

Transcript

Question 7 In a squared sheet, draw two triangles of equal areas such that (i) the triangles are congruent. What can you say about their perimeters?Two congruent triangles Here, ∆ABC ≅ ∆DEF Finding ar (ABC) ∴ ar (ABC) = 2 + 2 = 4 square units Finding ar (DEF) ∴ ar (DEF) = 2 + 2 = 4 square units ∴ ar (ABC) = ar (DEF) Thus, triangles are of equal areas and are congruent Now, Let’s check perimeter of both triangles As Δ ABC ≅ Δ DEF By CPCT AB = DE BC = EF AC = DF Adding (1), (2) & (3) AB + BC + AC = DE + EF + DF Perimeter of Δ ABC = Perimeter of Δ DEF Thus, perimeters of congruent triangles are also equal Question 7 In a squared sheet, draw two triangles of equal areas such that (ii) the triangles are not congruent. What can you say about their perimeters? Two triangles not congruent Here, ∆MNO ≇ ∆IJK Finding ar (MNO) ∴ ar (MNO) = 2 + 2 = 4 square units Finding ar (IJK) ∴ ar (IJK) = 2 + 2 = 4 square units Thus, ar (MNO) = ar (IJK) But ∆MNO ≇ ∆IJK Measuring Perimeter By measuring Perimeter, Perimeter of MNO > Perimeter of IJK So, Perimeter are not equal.