TO CONSTRUCT A TRIANGLE HAVING GIVEN THE PERIMETER AND
THE MEASURES OF TWO ANGLES.
------------------------------------------------------------------------------------------------------------------Type of Project: Observation/Construction
Grade: 9th
Govt. Girl’s High School, Ranpur.
Dt.19th Feb 08 to 26th Feb 08
Mr. Basudev Mishra.
Objective:
Students will be able to proof this construction can be proved with observation/
construction for their better understanding.
Material Required:
 Ruler
 Pencil
 Scissors
 Piece of Paper
 Protractor
Activity:
Students are divided into 5groups & are instructed to follow these steps.
Steps:
1. Students are instructed to draw an obtuse angle triangle in the paper, name it as
AB’C’ (name the obtuse angle as A).
2. Cut the triangle AB’C’ out of the paper.
3. Now take the vertex B’ & C’, fold in such a way that the vertices B’ & C’ coincides
with vertex A.
4. After folding, unfold the triangle AB’C’ & we will get points B, C, D & E.
5. Now draw segments BD, BA, CE & AC.
6. Now all the groups are instructed to measure
 Angles B’,C’, ABC & ACB.
 Sides BB’, CC’, AB, BC & AC.
Observation:
Groups
B’
C’
ABC ACB
1
370
230
740
460
3.1cm 4.4cm 3.1cm 3.9cm 4.4cm
2
310
230
620
460
4.3cm 5.3cm 4.3cm 5.6cm 5.3cm
3
0
35
0
36
0
70
0
72
5.6cm 5.5cm 5.6cm 3.8cm 5.5cm
4
200
660
400
1320
7.3cm 6.1cm 7.3cm 1.5cm 6.1cm
5
280
510
560
1020
4.9cm 4.2cm 4.9cm 1.7cm 4.2cm
BB’
CC’
AB
BC
Conclusion:
B’ = ½ ABC & C’=1/2ACB
BB’ = AB, CC’= AC & AB + BC + AC = BB’ + BC + CC’ = Perimeter
AC
Conclusion
B’ =1/2ABC
C’ =1/2ACB
Step of Construction
 Draw a line having length of perimeter & named it as DE.
 Construct an angles at D equal to ½ of one angle given.
 Construct another angles at E equal to ½ of other given angle.
 Draw lines from D & E with the constructed angles & they meet at A.
 Now draw the perpendicular bisector of sides AD & AE.
 Name the point B where the perpendicular bisector of AD meets DE. Similarly
name the point C where the perpendicular bisector of AE meets DE.
 Now joins AC & AC.
 Hence ABC is the required triangle.