Mathematical Theorems

Govt. Model High School Nabha

Topic Mathematical Theorems Prepared by Kulwant Kaur Math mistress

An isosceles triangle C

C

A

B

A

D

C

B

A

D

Result : - sides AB falls on side AC-> Angle B = Angle C Right bisector of Base BC passes through vertex A.

B

An isosceles Triangle •Objective:1.Angle opposite to equal sides are equal 2.Right bisector of bases passes through vertex •Material required:- pencil, ruler, black pen, glace paper and compass • Stops:1.Fold the triangle ABC such that b falls on C. 2.Press the two parts to obtain the oases. 3.When we open the paper we will see that the crease passer though vertex A. 4.Join AM • Results: - Sides AB falls exactly on side AC => Angle B = Angle C Right bisector of base BC passes through the vertex A.

A Parallelogram B

A

C

A C

D

B

A Parallelogram

•

Objective :opposite sides of a parallelogram are equal.

•

Material required: butter paper, pencil, ruler, colour

•

Stops:1.Draw a parallelogram ABCD as shown in fig.1 and paint with pink. Join B with ball point pen. Cut the ABCD a long BD and superimpose the Triangle DBC and triangle BDA as shown in fig. 2

•

Result :- we observe that triangle DBC cover the triangle BDA exactly and vertex C falls on A,D falls on B and B falls on D.It follows that AD=BC and AB=DC.

Diagonal Property of A Parallelogram C

D

A

I

B

A(C)

II

B(C)

Diagonal property of a Parallelogram • •

Topic : diagonal property of a parallelogram Objective: to verify the diagonal of a parallelogram bisect each other. • Material required: butter paper, pencil, ruler and color. • Stops (i) Draw any parallelogram of triangle ABCD on butter paper (ii) Draw diagonal ac and bd. Let the diagonal intersect on o. (iii) Draw horizontal line in triangle OAB and vertically line in triangle ODC. Shown in fig.1 (iv) Cut the triangle OCD and superimpose it on triangle AOB.Shown in fig. 2. • Results: - we see that triangle OCD cover exactly triangle AOB vertex C falls on A and D falls on B and O falls on O. => OA = OC and OB = OD. The diagonal bisector each other

Sides an Angle of a Triangle A

B

C

Sides and angle of a Triangle •

Objective: - To observe that grater of a triangle has greater angle opposite of it. • Material required: - Drawing sheet, pencil, ruler color and compass. • Stops : - (i) Draw any scalene triangle on drawing sheet. (ii) Paint angle A,B and C with different color. (iii) Cut of the angle A, angle B and angle C and compare them. • Result: - We observe that BC>AC>AB => Angle A> Angle B > Angle C

Area Of A Parallelogram b B

A

H

H

D

E

C b

B

A

E

F

Area of Parallelogram. • • •

Objective: - To Find the formula for the area of a parallelogram. Material Required: - Color, Pencil, Ruler and Cardboard Stops: - (i) Draw an parallelogram ABCD of base b and height h on a drawing sheet. (ii) From A draw AE CD paint triangle ADE with blue color and remaining part of a parallelogram with orange color. (iii) Cut of triangle AED and paste it in the position of BFC. • Result : - We observe that ABFE is rectangle and we observe that area of parallelogram Rectangle ABCD and area of rectangle ABFE is same. Area of parallelogram = Area of rectangle ABFE = Length X breadth =bXh = base X height Area of parallelogram = base X height

Area of Triangle A

A

h

h

B

b

C

B

C b

Area of Triangle • • •

Objective To find the formula for the area of triangle Material Required: - Drawing sheet, pencil, ruler and color. Stops : - (i) Draw and triangle ABC of base b and height h on a drawing sheet. (ii) Make horizontal lines with blue pen in it (iii) Mark on extra copy of triangle ABc from the the drawn horizontal line with pink color in it. (iv) Paste the pink copy triangle ABC in the postion triangle ACD. • Result: - We observe that triangle ABCD is a parallogram, we also note that the area of parallelogram ABCD consits of area of Triangle and are of its copy. Then Area of triangle ABC = ½ of area of parallelogram. = ½ Base X Height =½XBXH