Exercise 6.1 (Revised) - Chapter 6 - Triangles & Its Properties - Ncert Solutions class 7 - Maths

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Chapter 6 - Triangles & Its Properties | NCERT Solutions Class 7 Maths

Ex 6.1 Question 1.

In $\Delta \mathrm{PQR}, \mathrm{D}$ is the mid-point of $\overline{\mathrm{QR}}$.
$\overline{\mathrm{PM}}$ is $\qquad$
$\mathrm{PD}$ is $\qquad$
Is $\mathrm{QM}=\mathrm{MR}$ ?

Answer:

Given: QD = DR
$\therefore \overline{\mathrm{PM}}$ is altitude.
PD is median.
No, $\mathrm{QM} \neq \mathrm{MR}$ as $\mathrm{D}$ is the mid-point of $\mathrm{QR}$.
Ex 6.1 Question 2.

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

Answer:

(a) Here, $\mathrm{BE}$ is a median in $\triangle \mathrm{ABC}$ and $\mathrm{AE}=\mathrm{EC}$.

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

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

Ex 6.1 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 $\triangle \mathrm{ABC}$ and draw the median when $\mathrm{AB}=\mathrm{AC}$.
AL is the median and altitude of the given triangle.