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

__Question:__**Options:**

A. | Fig 1 and Fig 3 only | |

B. | Fig 2 and Fig 3 only | |

C. | Fig 1, Fig 2 and Fig 4 only | |

D. | Fig 1, Fig 2 and Fig 3 only |

**Answer: Option A**

: A

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. Fig1:

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∘

ΔPQRis an obtuse angled triangle as one of the angles measures 130°.

2. Fig 2:

ΔABCis 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 angledtriangle.

3. Fig3:

ΔXYZis an isosceles as well as an obtuse angled triangle as angleY measures 110°.

4. Fig4:

ΔMNOis an isosceles as well as a right angled triangle.

Hence, only Fig1and Fig3are isosceles as well as obtuse angledtriangles.

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## More Questions on This Topic :

: Let the exterior angles of the triangle be x, y and z respectively.

Then by exterior angle property,interior angles of the triangle will be (180−x)∘, (180−y)∘, (180−z)∘ Using angle sum property of a triangle, (180- x) + (180- y) + (180- z) = 180 540-(x + y + z) =180 Therefore, x + y + z = 360∘

**The square of the hypotenuse is equal to the sum of the squares of the other two sides. This relation holds for all types of triangles.**

__Question 6.__- True
- False

**Answer: Option B**

: B

The square of the hypotenuse is equal to the sum of the squares of the other two sides. This relation holds only in right-angled triangles.

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