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Full exercise on Practical Geometry, fully solved. This is a video tutorial for 7th class NCERT CBSE students. For other educational stuff, subscribe and press bell icon.

Practical Geometry 10.5

CONSTRUCTING A RIGHT-ANGLED TRIANGLE WHEN THE LENGTH OF ONE LEG AND ITS HYPOTENUSE ARE GIVEN (RHS CRITERION)

Here it is easy to make the rough sketch. Now, draw a line as per the given side. Make a right angle on one of its points. Use compasses to mark length of side and hypotenuse of the triangle. Complete the triangle. Consider the following: EXAMPLE 4 Construct ΔLMN, right-angled at M, given that LN = 5 cm and MN = 3 cm.

EXERCISE 10.5

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

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

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

Miscellaneous questions

Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and, say why you cannot construct them. Construct rest of the triangles.

Triangle Given measurements
1. ΔABC m∠A = 85°; m∠B = 115°; AB = 5 cm.
2. ΔPQR m∠Q = 30°; m∠R = 60°; QR = 4.7 cm.
3. ΔABC m∠A = 70°; m∠B = 50°; AC = 3 cm.
4. ΔLMN m∠L = 60°; m∠N = 120°; LM = 5 cm.
5. ΔABC BC = 2 cm; AB = 4 cm; AC = 2 cm.
6. ΔPQR PQ = 3.5 cm.; QR = 4 cm.; PR = 3.5 cm.
7. ΔXYZ XY = 3 cm; YZ = 4 cm; XZ = 5 cm
8. ΔDEF DE = 4.5cm; EF = 5.5cm; DF = 4 cm.

WHAT HAVE WE DISCUSSED?

In this Chapter, we looked into the methods of some ruler and compassesconstructions.

1. Given a line l and a point not on it, we used the idea of ‘equal alternate angles’ in a transversal diagram to draw a line parallel to l.

We could also have used the idea of ‘equal corresponding angles’ to do the construction.

2. We studied the method of drawing a triangle, using indirectly the concept of congruence of triangles.

The following cases were discussed:

(i) SSS: Given the three side lengths of a triangle.

(ii) SAS: Given the lengths of any two sides and the measure of the angle between these sides.

(iii) ASA: Given the measures of two angles and the length of side included between them.

(iv) RHS: Given the length of hypotenuse of a right-angled triangle and the length of one of its legs.

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