Page 170 - Maths Skills - 8

168 Maths

3. In the given figure, the bisectors of ∠R and ∠P of quadrilateral TRAP meet AP and TR produced at S and
1
Q respectively. Prove that ∠S + ∠Q = (∠ART + ∠TPA).

2
R
T Q
3
4

2
S 1 A
P

Word Stock
Adjacent Alternative Corresponding Diagonal Parallel Perpendicular
Bisect Dimension Concave Convex Opposite Regular

Activity

Objective: To verify that the sum of four angles of a quadrilateral is 360º.

Pre-Requisite Knowledge: Angle at a point is 360º.

Materials Required: Cardboard, geometry box, coloured paper, white drawing sheet, sketch pens, a pair of
scissors, fevicol. C

Procedure: 1. Take a rectangular piece of cardboard and call it a baseboard. 11 cm
2. Cut two congruent quadrilaterals from white drawing sheet. D
3. Colour the four angles of both the quadrilaterals with different 10.5 cm
colours after drawing circular arcs of same radius, as shown in Fig. 7 cm

A 7 cm B

4. Paste one of the quadrilaterals on the baseboard and cut the four coloured angles from the other
quadrilateral.
5. Place the cutouts of angles of the quadrilateral in such a way that the four
vertices coincide at a point say O, thereby forming a complete angle at the O
point O, as shown in Fig.
6. Record your observations to verify it by measuring the angles with protractor.

Observations: Angle 1 = _____________________________________________.

Angle 2 = _____________________________________________.

Angle 3 = _____________________________________________.

Angle 4 = _____________________________________________.