Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same

Solution:

The median and the altitude of an isosceles triangle can be the same.

Let's draw an isosceles triangle and draw a line that divides them into two equal parts.

The two sides of this triangle are equal because it is an isosceles triangle and the line drawn is perpendicular to the triangle and also it divides the base into two equal parts.

Let's analyze it below.

• Draw a triangle PQR  with PQ = PR and then draw a line segment PS perpendicular to QR.
• PS is the altitude of the triangle.
• It can be observed that the length of QS and SR is also the same by measurement.
• Thus, S is the midpoint of QR. Therefore, PS is also a median of this triangle.

Hence, we can say that PS is the altitude and median of the isosceles triangle PQR.

☛ Check: NCERT Solutions for Class 7 Maths Chapter 6

Video Solution:

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same

NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.1 Question 3

Summary:

We have verified by drawing a diagram that the median and altitude of an isosceles triangle can be the same.

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