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Question

Which of the following triangles are isosceles as well as obtuse-angled triangles?


A

Fig 1 and Fig 3 only

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B

Fig 2 and Fig 3 only

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C

Fig 1, Fig 2 and Fig 4 only

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D

Fig 1, Fig 2 and Fig 3 only

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Solution

The correct option is A

Fig 1 and Fig 3 only


An obtuse angled triangle is the triangle in which one of the angles is greater than 90.
An isosceles triangle is the triangle in which two sides are equal.
1. Fig 1:
ΔPQR is isosceles [PQ=PR]
Q=R
[ angles opposite to equal sides of a triangle are equal]
P+Q+R =180
[angle sum property of a triangle]
P+25 +25 =180
P=180 50=130
ΔPQR is an obtuse angled triangle as one of the angles measures 130°.
2. Fig 2:
ΔABC is isosceles [AB=AC]
Similarly as above, we can find the angles of this triangle.
A=35,B=C=72.5
Since all angles are less than 90, ΔABC is an acute angled triangle.
3. Fig 3:
ΔXYZ is an isosceles as well as an obtuse angled triangle as angle Y measures 110°.
4. Fig 4:
ΔMNO is an isosceles as well as a right angled triangle.
Hence, only Fig 1 and Fig 3 are isosceles as well as obtuse angled triangles.


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