Free The Triangle and Its Properties 02 Practice Test - 7th grade 

A median is line joining a vertex of a triangle to the mid-point of the opposite side.

A median connects a vertex of a triangle to the mid point of the opposite side.
An altitude is a perpendicular on one of the sides from the opposite vertex.
As OB is the altitude, B may or may not be the midpoint of CE.

A triangle with all the three angles less than ${60}^{\circ }$ is not possible, as the sum of all the angles of a triangle is ${180}^{\circ }$​.

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 $(180-x{)}^{\circ }$​, $(180-y{)}^{\circ }$​​, $(180-z{)}^{\circ }$​​

Using angle sum property of a triangle,

(180 - x) + (180 - y) + (180 - z) = 180

540 - (x + y + z) = 180

Therefore, x + y + z = ${360}^{\circ }$​

Sum of lengths of any two sides of a triangle should always be greater than the third side.

Here, 2 + 3 = 5
Therefore, this triangle is not possible.

By Exterior angle property of triangles,
x + y = $\angle$A + $\angle$B
         = ${50}^{\circ }$​ + ${70}^{\circ }$
         = ${120}^{\circ }$

The third side of a triangle must be greater than the difference between the other two sides.

x + y + $\angle$ACB = ${180}^{\circ }$  (Angles on a straight line)​

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.

An obtuse angled triangle is the triangle in which one of the angles is greater than ${90}^{\circ }.$ 
An isosceles triangle is the triangle in which two sides are equal.
1. Fig 1:
$\Delta PQR$  is isosceles $[\because PQ=PR]$
         $\Rightarrow \angle Q=\angle R$
[$\because$ angles opposite to equal sides of a triangle are equal]
$\angle P+\angle Q+\angle R={180}^{\circ }$ 
[angle sum property of a triangle]
$\angle P+{25}^{\circ }+{25}^{\circ }={180}^{\circ }$
$\Rightarrow \angle P={180}^{\circ }-{50}^{\circ }={130}^{\circ }$ 
$\Delta PQR$ is an obtuse angled triangle as one of the angles measures 130°.
2. Fig 2:
$\Delta ABC$ is isosceles $[\because AB=AC]$
Similarly as above, we can find the angles of this triangle.
$\angle A={35}^{\circ },\angle B=\angle C={72.5}^{\circ }$ 
Since all angles are less than ${90}^{\circ }$, $\Delta ABC$ is an acute angled triangle.
3. Fig 3:
$\Delta XYZ$ is an isosceles as well as an obtuse angled triangle as angle Y measures 110°.
4. Fig 4:
$\Delta MNO$ 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.