Test: The Triangle and Its Properties

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

A/an median  connect a vertex of a triangle to the mid-point of the opposite side.

A triangle can have 3 altitudes

By Pythagoras property,
AB² = AC² + BC²
= 5² + 12² = 25 + 144 = 169 = 132
or AB²= 132. So, AB = 13 or the length of AB is 13 cm.

In triangle PQR, for vertex Q the line joining the other two vertex is the side opposite to Q.

for example, 

The vertex opposite to side RT is S.

Step-by-step explanation:

In the given question,

We have a triangle RST which has sides RS, ST and TR.

We know that a triangle consists three vertices and three sides each of which is particularly opposite to any one of the side of the triangle and vice-versa.

Therefore, we can see here that in the triangle RST.

The side RS is opposite to the vertex T.

The side ST is opposite to the vertex R.

and,

The side TR is opposite to the vertex S.

Hence, the correct answer will be S as side RT is opposite to S.

In Δ PQR, PM is altitude

An exterior angle of a triangle is equal to the sum of the opposite interior angles

x^o = 70^o + 50^o

x^o = 120^o .

So option C is the correct answer. 

An exterior angle of a triangle is equal to the sum of the opposite interior angles

So in the given figure 

110^o = 50^o + x 

110^o - 50^o = x 

60^o = x 

So option B is correct answer. 

An exterior angle of a triangle is equal to the sum of the opposite interior angles

So in the given figure 

80^o = 30^o + x 

it implies x = 50^o. 

The sum of the angles of a triangle is 180 degrees. As the ratio of the angles of the triangle is 4:5:9 they can be taken to be 4x, 5x and 9x. 4x + 5x + 9x = 180

=> 18x = 180

=> x = 10

This gives the angles of the triangle as 4*10=40,

5*10=50 and 9*10=90 degrees.

a²+b²=c²

we find 3²+4²=5²

9 + 16 = 25

So, these sides also cause it to be a right triangle.

One angle of the triangle = 110°
Let the other two angles each be x
Sum of all the angles of a triangle = 180°
x + x + 110 = 180
2x = 180 - 110
2x = 70
x = 35°
The other two angles are 35°, 35°.

Let the angles be x
sum of the angles of a triangle=180

5x+3x+x=180
9x=180
x=20
angle I = 5x = 5*20 = 100
angle II = 3x = 3*20 = 60
angle III = x = 20

Since the sides of the isosceles triangle are equal the line drawn from vertex to middle of the opposite side which is median is perpendicular. And altitude is also perpendicular . So both are the same in the isosceles triangle.