If we draw a median AD in ∆ABC, are the altitudes of ∆ADB and ∆ADC equal in length? Justify.
[3 marks]

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Solution

Yes.
(0.5 mark)

(0.5 mark)

The median AD will divide the ∆ABC into 2 triangles ∆ADB and ∆ADC. These two triangles, as shown in the figure will have the same altitude AN as the altitude is the perpendicular distance from the vertex to the base of the triangle.
The foot of the perpendicular can be inside as well as outside the triangle as shown in the figure. (Note: The median of the triangle divides it into 2 triangles with equal area.)
(2 marks)

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IF AD is a median of a triangle ABC, then prove that triangles ADB and ADC are equal in area. If G is the midpoint of median AD, prove that ar $(△ B G C) = 2 a r (△ A G C) .$

In a triangle ABC, AC = AB and the altitude AD bisects BC. Prove that ΔADC ≅ ΔADB.

In the figure, two sides AB, BC and the median AD of ΔABC are respectively equal to two sides PQ, QR and median PS of ΔPQR. Prove that

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Does it follow that triangles ABC and PQR are congruent?

Q. If we draw a median AD in ∆ABC, are the altitudes of ∆ADB and ∆ADC equal in length? Justify.

If we draw a median AD in ∆ABC, are the altitudes of ∆ADB and ∆ADC equal in length? Justify. [2 MARKS]

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If we draw a median AD in ∆ABC, are the altitudes of ∆ADB and ∆ADC equal in length? Justify. [3 marks]

If we draw a median AD in ∆ABC, are the altitudes of ∆ADB and ∆ADC equal in length? Justify.
[3 marks]