CBSE Book Class 7 Maths Activity 8

(a) To verify by paper cutting and superimposing that diagonal of a parallelogram divides it into two congruent triangles.

(b) To verify using a squared paper that all congruent triangles are equal in area but the triangles equal in area may not be congruent.

Learning Objective : (1) To understand that diagonal of a parallelogram divides it into two congruent triangles.

(2) To understand that all congruent triangles are equal in area but the triangles equal in area may not be congruent.

Pre-requisite : Knowledge of a parallelogram and its a diagonals. Idea of congruent triangles.

Materials Required : Squared papers, a ruler, sketch pens and a pair of scissors.

Procedure : (a)

Step 1. Take a squared paper.

Step 2. Draw a parallelogram ABCD on it. [Fig 8(a)]

Step 3. Join diagonal AC. [Fig. 8(b)]

Step 4. Cut out the parallelogram ABCD.

Step 5. Cut the parallelogram along the diagonal AC. [Fig. 8(c)]

Step 6. Place the triangle D ADC on D ABC such that AD coincides with CB and CD coincides with
AD.

Step 7. Repeat the activity by cutting across the other diagonal BD of the parallelogram ABCD and superpose one triangle on the other.

Observations :
(i) When cut along AC, the two triangles ABC and ADC cover each other completely..(Yes/No)

(ii) Are the triangles ABC and ADC congruent? .......................... (Yes/No).

(iii) When cut along BD, are the triangles thus obtained congruent?………….. (Yes/No)

(iv) The diagonal of a parallelogram divides it into two .................... triangles.

Procedure : (b)

Step 1. Count the number of squares of triangles ABC and ADC which you have shown congruent in the Procedure (a).

Observations : (i) Number of unit squares in DABC = .................

Please refer to the link below - CBSE Class 7 Maths Activity 8