class 9 / maths

CLASS 9 / PRACTICE QUESTIONS

AREA OF PARALLELOGRAM AND TRIANGLE

Q.1) ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F.

 Show ar (∆ ACB) = ar(∆  ACF).

Q.2) In the given figure, PQR and QST are two triangles such that S is the mid-point of QR. and QT // PR.

Q.3) ABCD is a Quadrilateral. A line through D, parallel to AC, meets BC produced in P as shown in figure. Prove that ar(∆ ABP) = ar(Quad ABCD).

Q.4) In a triangle ABC, D is the mid-point of AB. P is any point of BC. CQ || PD meets AB in Q. Show that

Q.5) Prove that area (∆ AFG) = ½ area(BDEF).

Q.6) If D, E and F are the mid points of sides AB, BC and AC respectively then show that

(i) area (∆ ADE) = area (∆ AFE)

(ii) area (∆ BDE) = area (∆ CEF)

(iii) area (ADEF) = ½ area (∆ ABC)

Q7) In ∆ ABC, D is the mid-point of BC, E is the mid-point of BD. If „O‟ is the mid-point of AE, prove that

 ar (∆ BOE) = (1/8) ar (∆ ABC).

Q.8) In the given figure E is the midpoint of BC and D is the midpoint of AE. PEDB and QEDC are parallelograms then show that area (∆ PBE) + area (∆ QCE) = ½ area (∆ ABC).

Q.9) In the given figure, if BE||CF and area (ABCE) = area (BDEF) then prove that AD|| BE.

Q.10) The area of parallelogram PQRS is 152 cm². Find the area of rectangle PQXY. If the base PQ = 19 cm, find the height of the parallelogram.

CLASS 10 / PHYSICS/ VIDEO LINK

SPHERICAL MIRRORS.....................

https://www.youtube.com/watch?v=7zv-4Zh-9R4

https://www.youtube.com/watch?v=T5sspQR4TIs

class 9 / maths/ ch-9 (AREA OF PARALLELOGRAM & TRIANGLE)

click the below link to view the document.................

http://ncert.nic.in/ncerts/l/ieep209.pdf

class 10 / spherical mirrors

Spherical Mirrors

A mirror whose polished, reflecting surface is a part of a hollow sphere of glass or plastic is called a spherical mirror.

The spherical mirror is classified as:

• Concave mirror

• Convex mirror

1. concave mirror – a spherical mirror whose reflecting surface is bent inwards is called concave mirror.

2. convex mirror - a spherical mirror whose reflecting surface is bent outwards is called concave mirror.\

Terms related to spherical mirrors:

1. Pole

·         The center of a spherical mirror is called its pole .

·         It lies on the reflecting surface of a spherical mirror

·         Is represented by letter P .

2.      Centre of curvature

·         The reflecting surface of a spherical mirror forms a part of a sphere. This sphere has a centre. This point is called the centre of curvature of the spherical mirror.

·         It is represented by the letter C.

·         The centre of curvature is not a part of the mirror. It lies outside its reflecting surface.

·         The centre of curvature of a concave mirror lies in front of it. However, it lies behind the mirror in case of a convex mirror.

3.      Radius of curvature

·         The radius of the sphere of which the reflecting surface of a spherical mirror forms a part, is called the radius of curvature of the mirror.

·          It is represented by the letter R.

·         The distance PC is equal to the radius of curvature.

4.      Principal axis

·         Straight line passing through the pole and the centre of curvature of a spherical mirror is called principle axis of the mirror.

·         The principal axis is normal to the mirror at its pole.

5.      Aperture of the mirror

·         Portion of the mirror from which reflection of light actually takes place is called the aperture of the mirror.

·         Aperture of the mirror actually represents the size of the mirror.

·         Distance MN represents the aperture.

Principle focus and focal length of a Spherical Mirrors

• Consider light rays parallel to the principal axis are falling on a concave mirror. By observing the reflected rays we conclude that they are all intersecting at a point F on the principal axis of the mirror. This point is called the principal focus of the concave mirror.
• In case of convex mirror rays get reflected at the reflecting surface of the mirror and these reflected rays appear to come from point F on the principle axis and this point F is called principle focus of convex mirror.
• The distance between the pole and the principal focus of a spherical mirror is called the focal length. It is represented by the letter f.
• There is a relationship between the radius of curvature R, and focal length f, of a spherical mirror and is given by R=2f which means that that the principal focus of a spherical mirror lies midway between the pole and centre of curvature.

Characteristics of Concave and a Convex Mirror

Convex Mirror	Concave Mirror
Reflecting surface is curved outwards.	Reflecting surface is curved inwards.
The focus is virtual as the rays of light after reflection appear to come from the focus.	The focus is real as the rays of light after reflection converge at the focus.
The focus lies behind the mirror	The focus is in front of the mirror
Diverging mirror	Converging mirror
Image Cann’t be projected on a screen	Image Can be projected on a screen

 Note :  A concave mirror is also known as a converging mirror as the parallel rays of light after getting reflected from the concave mirror converge at the focus.

A convex mirror is known as a diverging mirror as the parallel rays of light after reflection appear to come from a point, i.e., the rays diverge after reflection.