The Triangle and its Properties - Solutions

 CBSE Class –VII Mathematics

NCERT Solutions
Chapter 6 The Triangle and its Properties (Ex. 6.1)

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Question 1. In Δ$\mathrm{\Delta }$PQR, D is the mid-point of QR¯¯¯¯¯¯¯¯.$\overline{\text{QR}}.$
PM¯¯¯¯¯¯¯¯$\overline{\text{PM}}$ is _______________
PD is ________________
Is QM = MR ?

Answer: Given: QD = DR

∴$\therefore$ PM¯¯¯¯¯¯¯¯$\overline{\text{PM}}$ is altitude.

PD is median.

No, QM ≠$\ne$ MR as D is the mid-point of QR.

Question 2. Draw rough sketches for the following:

1. In Δ$\mathrm{\Delta }$ABC, BE is a median.
2. In Δ$\mathrm{\Delta }$PQR, PQ and PR are altitudes of the triangle.
3. In Δ$\mathrm{\Delta }$XYZ, YL is an altitude in the exterior of the triangle.

Answer: (a) Here, BE is a median in ΔABC$\mathrm{\Delta }\text{ABC}$ and AE = EC.

(b) Here, PQ and PR are the altitudes of the Δ$\mathrm{\Delta }$PQR and RP ⊥$\mathrm{\perp }$ QP.

(c) YL is an altitude in the exterior of Δ$\mathrm{\Delta }$XYZ.

Question 3. Verify by drawing a diagram if the median and altitude of a isosceles triangle can be same.

Answer: Isosceles triangle means any two sides are same.

Take ΔABC$\mathrm{\Delta }\text{ABC}$ and draw the median when AB = AC.

AL is the median and altitude of the given triangle.