Answer:
option (2) and (5) are correct.
ΔABC ≅ ΔJLK
ΔDEF ≅ ΔGHI
Step-by-step explanation:
Given four right angled triangle with measure of sides.
We have to check for the pairs of triangle to be similar.
Two triangles are said to be similar if their corresponding angles are equal or their corresponding sides are same ratio.
Consider, ΔABC and ΔJLK.
∠C = ∠L = 90° (given)
Also ratio of corresponding sides are same ratio, that is
[tex]\frac{AC}{LJ}=\frac{14}{7}=\frac{2}{1}[/tex]
Also, [tex]\frac{CB}{KL}=\frac{20}{10}=\frac{2}{1}[/tex]
Thus, ΔABC ≅ ΔJLK.
Option (5) is correct.
Consider, ΔDEF and ΔGHI.
∠I = ∠F = 90° (given)
Also ratio of corresponding sides are same, that is
[tex]\frac{DF}{GI}=\frac{8}{12}=\frac{2}{3}[/tex]
Also, [tex]\frac{EF}{HI}=\frac{10}{15}=\frac{2}{3}[/tex]
Thus, ΔDEF ≅ ΔGHI.
Option (2) is correct.
Thus, option (2) and (5) are correct.
