If AM and CN are perpendiculars on the diagonal BD of a parallelogram ABCD, Is ∆AMD ≅ ∆CNB? Give reasons.
Solution:
Given, ABCD is a parallelogram.
AM and CN are perpendiculars on the diagonal BD.
We have to determine if ∆AMD ≅ ∆CNB
We know that the opposite sides are equal in a parallelogram.
AD = BC ----------- (1)
AB = DC ----------- (2)
Considering triangles AMD and CNB,
From (1), AD = BC
Given, AM and CN are perpendicular on the diagonal BD
∠AMB = ∠CNB = 90°
The opposite sides of a parallelogram are parallel.
Considering AD || BC and BD as transversal,
∠ADM = ∠NBC
AAS criterion states that two triangles are congruent if any two angles and the non-included side of one triangle are equal to the corresponding angles and the non-included side of the other triangle.
By AAS criterion, ∆AMD ≅ ∆CNB
✦ Try This: In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ. Show that APCQ is a parallelogram.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Solved Problem 25
If AM and CN are perpendiculars on the diagonal BD of a parallelogram ABCD, Is ∆AMD ≅ ∆CNB? Give reasons.
Summary:
If AM and CN are perpendiculars on the diagonal BD of a parallelogram ABCD, ∆AMD ≅ ∆CNB by AAS criterion.
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