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The Triangle And Its Properties

Question
CBSEENMA7000847
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Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

Solution

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Draw a line segment AD perpendicular to BC. It is an altitude for this triangle. It can be observed that the length of BD and DC is also same. Therefore, AD is also a median of this triangle.

Some More Questions From The Triangle and its Properties Chapter

Is it possible to have a triangle with the following sides?

(i) 2 cm, 3 cm, 5 cm (ii) 3 cm, 6 cm, 7 cm

(iii) 6 cm, 3 cm, 2 cm

Take any point O in the interior of a triangle PQR. Is

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(i) OP + OQ > PQ?

(ii) OQ + OR > QR?

(iii) OR + OP > RP?

AM is a median of a triangle ABC.

Is AB + BC + CA > 2 AM?

(Consider the sides of triangles ΔABM and ΔAMC.)

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ABCD is quadrilateral.

Is AB + BC + CD + DA >AC + BD?

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ABCD is quadrilateral.

Is AB + BC + CD + DA < 2 (AC + BD)?

The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?

PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.

ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC

A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.

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Which of the following can be the sides of a right triangle?

(i) 2.5 cm, 6.5 cm, 6 cm

(ii) 2 cm, 2 cm, 5 cm

(iii) 1.5 cm, 2 cm, 2.5 cm

In the case of right-angled triangles, identify the right angles.

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