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On January 25, 2024, 11:35 AM

Exercise 10.5 - Chapter 10 Practical Geometry class 7 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Construct the right angled ΔPQR, where m∠Q = 90°, QR = 8 cm and PR = 10 cm.

Answer:

A rough sketch of ΔPQR is as follows.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1478/Chapter%2010_html_m1d6801fa.jpg

The steps of construction are as follows.

(i) Draw a line segment QR of length 8 cm.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1478/Chapter%2010_html_m2c796148.jpg

(ii) At point Q, draw a ray QX making 90º with QR.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1478/Chapter%2010_html_m620fc7f9.jpg

(iii) Taking R as centre, draw an arc of 10 cm radius to intersect ray QX at point P.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1478/Chapter%2010_html_621bc5c1.jpg

(iv) Join P to R. ΔPQR is the required right-angled triangle.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1478/Chapter%2010_html_bab73a5.jpg

Question 2:

Construct a right-angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.

Answer:

A right-angled triangle ABC with hypotenuse 6 cm and one of the legs as 4 cm has to be constructed. A rough sketch of ΔABC is as follows.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1481/Chapter%2010_html_m5ba48bf4.jpg

The steps of construction are as follows.

(i) Draw a line segment BC of length 4 cm.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1481/Chapter%2010_html_43e522e8.jpg

(ii) At point B, draw a ray BX making an angle of 90º with BC.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1481/Chapter%2010_html_61273909.jpg

(iii) Taking C as centre, draw an arc of 6 cm radius to intersect ray BX at point A.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1481/Chapter%2010_html_26ab48d5.jpg

(iv) Join A to C to obtain the required ΔABC.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1481/Chapter%2010_html_1ad19c5.jpg

Question 3:

Construct an isosceles right-angled triangle ABC, where, m∠ACB = 90° and AC = 6 cm.

Answer:

In an isosceles triangle, the lengths of any two sides are equal.

Let in ΔABC, AC = BC = 6 cm. A rough sketch of this ΔABC is as follows.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1483/Chapter%2010_html_54aefdd5.jpg

The steps of construction are as follows.

(i) Draw a line segment AC of length 6 cm.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1483/Chapter%2010_html_m5926068.jpg

(ii) At point C, draw a ray CX making an angle of 90º with AC.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1483/Chapter%2010_html_mf5e9cc4.jpg

(iii) Taking point C as centre, draw an arc of 6 cm radius to intersect CX at point B.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1483/Chapter%2010_html_602e6a39.jpg

(iv) Join A to B to obtain the required ΔABC.

https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/40/1483/Chapter%2010_html_67269803.jpg

Also Read : Exercise-11.1-Chapter-11-Perimeter-&-Area-class-7-ncert-solutions-Maths

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