In the figure given below, there are two triangles such that they have five pairs of congruent parts but still, the triangles are not ____.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

In the figure given below, there are two triangles such that they have five pairs of congruent parts but still, the triangles are not congruent.
Question Image

Check for congruency for

Δ M L N

Δ G H F,

From

Δ M L N

Δ G H F,

we have,

∠ L M N = ∠ G H F ∠ M L N = ∠ F G H ∠ L N M = ∠ G F H

From the above equations, all the angles of triangles are equal.
Also from

Δ M L N

Δ G H F,

L M = F G M N = G H

L N ≠ F H

From the above equations, only two sides are equal out of three sides.
Therefore, by the SSS property of congruence, both triangles are not congruent.
Thus, in the figure given above, there are two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.

Watch 3-min video & get full concept clarity