Exercise 5.2

1. In ΔABC, D is the midpoint of BC.

(i). AD is the .

(ii) AE is the .

2. Name the triangle in which the two altitudes of the triangle are two of its sides.

Solution:

In a right-angled triangle: The two sides forming the right angle are perpendicularparallel to each other

These sides are also altitudesmedians of the triangle

Therefore, a Right-angledEquilateralIsosceles triangle has two altitudes that are also its sides.

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

Solution:

Let's understand what a median is: A median connects a vertexside to the midpointendpoint of the opposite side

Properties of a median: It divides the triangle into two parts of equalunequal areas

It always lies insideoutside the triangle

Therefore, YesNo, a median always lies in the interior of the triangle.

4. Does an altitude always lie in the interior of a triangle?

Solution:

Let's understand what an altitude is: An altitude is the perpendicularparallel line from a vertex to the opposite side

Consider different types of triangles: In acute-angled triangles: altitudes lie insideoutside

In right-angled triangles: two altitudes lie alongoutside the sides

In obtuse-angled triangles: one altitude lies outsideinside the triangle

Therefore, NoYes, an altitude does not always lie in the interior of a triangle.

5. (i) Write the side opposite to vertex Y in ΔXYZ.

Solution:

In ΔXYZ: The side opposite to vertex Y is XZYZXY

(ii) Write the angle opposite to side PQ in ΔPQR.

In ΔPQR: The angle opposite to side PQ is ∠R∠P∠Q

(iii) Write the vertex opposite to side AC in ΔABC.

In ΔABC: The vertex opposite to side AC is BAC