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01 Nov 2020, 00:48
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Is triangle ABC a right-angled \(\triangle\), if BD=DC and \(\angle ACB =60\)?
(1) AB is parallel to DE.
(2) D is the midpoint of AC.
Chetan's questions
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05 Nov 2020, 00:46
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chetan2u
We are given that BD=DC and \(\angle ACB =60\)
(1) AB is parallel to DE.
AB || DE. Since DE makes a perpendicular on BC, AB will also make a perpendicular on BC.
Thus ABC is a right-angled triangle.
(2) D is the midpoint of AC.
We are not required to know related theorems in GMAT, so there has to be a simpler way.
Let us take \(\triangle BDC\) => \(BD=DC\), so \(\angle DBC = \angle DCB = 60\), so \(\angle BDC = 180-60-60=60\)
Let us now take \(\triangle BDA\) => \(\angle BDA = 180-\angle BDC =180-60=120\),\(BD=DA\), so \(\angle DBA = \angle DAB = \frac{60}{2}=30\), so \(\angle BDA=30\)
\(\angle ABC = \angle ABD+\angle DBC=60+30=90\)
Thus ABC is a right-angled triangle.
D
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General Discussion
Neha2404
Joined: 07 Mar 2020
Last visit: 27 Oct 2025
Posts: 118
Given Kudos: 78
Location: India
Concentration: Finance, Accounting
Schools: IIMA PGPX'22 ISB'22 IIMB EPGP'22 Kellogg '22
01 Nov 2020, 01:32
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IMP-D
Statement-1
If DE Is parellel to DE
Then angle BAC = angel EDC
ANgle EDC Is =30
So BAC is -30
Angle ABC=180-30-60
=90
Sufficient
Statement 2
D is mid point of AC
Means AD =AC= BD = 2
And triangle BDC
Angle -CBD=60
And in angle D is 90
According to right angle property when a perpendicular draw on hypotension it divide equally
Sufficient
Posted from my mobile device
Statement-1
If DE Is parellel to DE
Then angle BAC = angel EDC
ANgle EDC Is =30
So BAC is -30
Angle ABC=180-30-60
=90
Sufficient
Statement 2
D is mid point of AC
Means AD =AC= BD = 2
And triangle BDC
Angle -CBD=60
And in angle D is 90
According to right angle property when a perpendicular draw on hypotension it divide equally
Sufficient
Posted from my mobile device
