Practicals I to V of MATH-2

Practicals

Practical No.1

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Aim:

Cut out two identical right angled triangles. Name the vertices of the triangles as A, B, C on both sides. Draw the altitude on the hypotenuse of one of them. Name the foot of the perpendicular as D. Cut the triangle on its altitude and obtain two triangles. State the correspondences by which the three triangles are similar with one another.

Observation table

For ∆ABC	For ∆BDC	For ∆ADB
∠ABC=90°	∠BDC=90°	∠ADB=90°
∠BAC=60°	∠DCB=60°	∠DBA=90°
∠ACB=30°	∠CBD=60°	∠BAD=60°

with the above observation

  

In ∆ABC and ∆BDC

under ABC ↔ BDC

∠ABC≅∠BDC

∠BCA≅∠DCB

∠CAB≅∠CBD

∴∆ABC~∆BDC

(By A-A-A test of similarity)

In ∆ABC and ∆ADB

under ABC ↔ ADB

∠ABC≅∠ADB

∠BCA≅∠DBA

∠CAB≅∠BAD

∴∆ABC~∆ADB

(By A-A-A test of similarity)

In ∆BDC and ∆ADB

under BDC ↔ ADB

∠BDC≅∠ADB

∠DCB≅∠DBA

∠CBD≅∠BAD

∴∆BDC~∆ADB

(By A-A-A test of similarity)

Conclusion:

Thus,the theorem of similarity of the right angled traingle is verified through practical.

Practical No.2

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Aim:

Draw a circle. Take three points - one on the circle, one in its interior and one in its exterior. Prepare a table, showing rough figures and stating how many tangents can be drawn to the circle through each of the three points.

Observation table

Sr.no	Rough Figure	Location of point with respect to the circle	Number of tangents that can be drawn
1		Point P lies in the interior of the circle	No tangent
2		Point Q lies on the circle	One tangent
3		Point R lies in the exterior of the circle	Two tangent

Conclusion:

1]From the point in the interior of the circle, zero tangent(s) can be drawn.
2] From the point on the circle,one tangent(s) can be drawn.
3] From the point outside the circle,two tangent(s) can be drawn.

Practical No.3

Aim:

Draw at least five different circles passing through two given distinct points indicating that innumerable circles can be drawn passing through them.

Do it yourself

Practical No.4

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Aim:

draw an angle and divide it into four equal parts using compass and ruler

Observation table

m∠ABC	m∠ABE	m∠EBD	m∠FBC	m∠DBF
120°	30°	30°	30°	30°

Conclusion:

Using the compass and ruler,the given angle can be divided into given number of equal parts.