# the medians of which triangle will always lie wholly in the interior of the triangle?

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## Does a median lie wholly in the interior of the triangle? (If you think that this is not true, draw a figure to show such a case).

2. Does a median lie wholly in the interior of the triangle? (If you think that this is not true, draw a figure to show such a case).

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Does a median lie wholly in the interior of the triangle? (If you think that this is not true, draw a figure to show such a case).

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**2.** Does a median lie wholly in the interior of the triangle? (If you think that this is not true, draw a figure to show such a case).

Yes, The median always lies in the interior of the triangle.

As we can see in all three cases the median lies inside the triangle.

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### Pankaj Sanodiya

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Yes, The median always lies in the interior of the triangle. As we can see in all three cases the median lies inside the triangle

### Posted by

### Shweta arya

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## Does a median lie wholly in the interior of the triangle? (If you think this is true then draw a figure to show such a case).

Does a median lie wholly in the interior of the triangle? (If you think this is true then draw a figure to show such a case).. Ans: Hint: A triangle is a 2-dimensional polygon that has three sides. \n \n \n \n \n Figure: TriangleCorners ...

## Does a median lie wholly in the interior of the triangle? (If you think this is true then draw a figure to show such a case).

Answer Verified 243.6k+ views 1 likes

**Hint:**A triangle is a 2-dimensional polygon that has three sides.

Figure: Triangle

Corners A, B, C are known as vertices of the triangle

△ABC △ABC .

AB, BC, CA are the sides of the triangle

△ABC △ABC . ∠ABC,∠BCA,∠CAB ∠ABC,∠BCA,∠CAB

are the interior angles of the triangle

△ABC △ABC , their sum is 180 ∘ 180∘ , i.e., ∠ABC+∠BCA+∠CAB= 180 ∘ ∠ABC+∠BCA+∠CAB=180∘

A line segment that joins the vertex of the triangle to the midpoint of the opposite side is called the median.

A triangle has three vertices and each vertex has an opposite side, thus, a triangle has three medians.

To check the given statement, draw a triangle and bisect its every side. Join the vertex and the midpoint of the opposite side i.e. median.

**Complete step-by-step answer:**

Step 1: Draw a triangle and bisect its one side.

To bisect the side of a triangle, you need a compass, a ruler, and a pencil.

First draw an obtuse triangle, a triangle whose one interior angle is more than

90 ∘ 90∘ .

Select the side which you want to bisect, here we have taken side AB.

Process 1: open the compass approximately more than the half of length of side AB. Taking vertex A as the center draws an arc, and then with the same length of the compass, taking vertex B as the center draws an arc such that it will intersect the previous arc.

Now join the vertex opposite to the side AB, i.e. vertex C and the intersection point of the arcs.

Thus the intersection point obtained on the side AB, i.e. E, is the midpoint of the side AB. And the line segment CE is the median.

Figure: Obtuse Triangle

∠ACB> 90 ∘ ∠ACB>90∘

Step 2: Draw the median to both sides of the obtuse triangle.

Similarly, bisect the side AC and join with the vertex B, and bisect the side BC and join with the vertex A.

Thus, the medians of the obtuse triangle are AF, BG, CE.

Figure: Obtuse Triangle

∠ACB> 90 ∘ ∠ACB>90∘

Thus the medians of an obtuse triangle lie wholly inside the triangle.

Step 3: Draw the medians of a right-angled triangle.

A right-angled triangle has one interior angle exactly equal to

90 ∘ 90∘ .

Bisect each side, by process 1 in step 1. And join the midpoint of the side with its respective opposite vertex.

Thus the medians of a right-angled triangle are AF, BG, CE.

Figure: right-angled triangle

∠ACB= 90 ∘ ∠ACB=90∘

Thus the medians of a right-angled triangle lie wholly inside the triangle.

Step 4: Draw the medians of an acute triangle.

An Acute triangle has all three interior angles less than

90 ∘ 90∘ .

Bisect each side, by process 1 in step 1. And join the midpoint of the side with its respective opposite vertex.

Thus the medians of an acute triangle are AF, BG, CE.

Figure: acute triangle

Thus the medians of an acute triangle lie wholly inside the triangle.

**Final answer: Yes, a median lies wholly in the interior of the triangle.**

**Note:**The intersection of the medians of a triangle called the centroid. It is represented by the point O in each triangle drawn above.

The centroid of the triangle divides each of the medians into

2:1 2:1 ratio.

The medians of the equilateral triangle are equal in length.

An equilateral triangle has its all three sides equal in length. All three interior angles are less than

90 ∘ 90∘

. Thus an acute triangle.

An isosceles triangle has two sides equal in length. All three interior angles are less than

90 ∘ 90∘

. Thus an acute triangle.

The scalene triangle has its all three sides unequal in length. All three interior angles are less than

90 ∘ 90∘

. Thus an acute triangle.

## Does a median always lie in the interior of the triangle

Yes a median always liein the interior of the triangle Note The intersection of the medians of a triangle called the centroid It is represented by the point O in each triangle drawn above The centroid of the triangle divides each of the medians into 21 ratio

Mathematics Class 7>Triangle and its Properties>Exercise - 2>Q 3

EASY Earn 100

Does a median always lie in the interior of the triangle?

Yes, a median lies wholly in the interior of the triangle.

Note: The intersection of the medians of a triangle called the centroid. It is represented by the point

O

in each triangle drawn above.

The centroid of the triangle divides each of the medians into

2:1 ratio.

## Important Questions on Triangle and its Properties

EASY

Mathematics Class 7>Triangle and its Properties>Exercise - 2>Q 4

Does a median always lie in the interior of the triangle? State Yes or No.

EASY

Mathematics Class 7>Triangle and its Properties>Exercise - 2>Q 5

Write the side opposite to vertex

Y in △XYZ . EASY

Mathematics Class 7>Triangle and its Properties>Exercise - 2>Q 5

Angle opposite to side

PQ in △PQR is ∠ ?

## Important Points to Remember on Triangle and its Properties

**1. Triangle:**

A triangle is a simple closed figure made up of three line segments.

**2. Classification of Triangles:**

(i) Based on the sides, triangles are of three types:

(a) A triangle having all three sides of same length is called an equilateral triangle.

(b) A triangle having at least two sides of equal length is called an isosceles triangle.

(c) If all the three sides of a triangle are of different length, the triangle is called a scalene Triangle.

(ii) Based on the angles, triangles are of three types:

(a) A triangle whose all angles are acute is called an acute-angled triangle.

(b) A triangle whose one angle is obtuse is called an obtuse-angled triangle.

(c) A triangle whose one angle is a right angle is called a right-angled triangle.

**3. Elements of a Triangle:**

The six elements of a triangle are its three angles and the three sides.

**4. Properties of the Lengths of the Sides of a Triangle:**

(i) The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

(ii) The difference between the lengths of any two sides of a triangle is smaller than the length of the third side.

**5. Median of Triangle:**

The line segment joining a vertex of a triangle to the mid-point of its opposite side is called a median of the triangle. A triangle has

3 medians.

**6. Altitude of a Triangle:**

The perpendicular line segment from a vertex of a triangle to its opposite side is called the altitude of the triangle.

**7. Properties of Triangle:**

(i) Angle Sum Property: The total measure of the three interior angles of a triangle is

180°

. This is called the angle sum property of a triangle.

(ii) Exterior Angle Property: The measure of any exterior angle of a triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of the triangle.

**8. Representation of Line, Line Segment and Ray:**

(i) LM= Line segment LM (ii) LM→= Ray LM (iii) LM↔= Line LM (iv) LM=

Length of Line segment of

LM .

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