Page 209 - Start Up Mathematics_7

Step 5: Unfold the paper and mark the point C as

shown. C C

Step 6: Finally, either fold or join BC to obtain an
equilateral ∆ ABC.

Justification: A D B A D B

Can you justify why ∆ ABC is equilateral?
[Hint: Since AB coincides with AC (as B lies on C),

∴ AB = AC and ∆ ADC ≅ ∆ BDC (why?)
Hence, AC = BC.]

Case II: SAS criterion

Construction of a triangle when lengths of two of its sides and an included angle are given
Let’s construct a triangle ABC in which AB = 5.1 cm, AC = 4.8 cm and ∠ BAC = 60º.

Construction: Draw a rough sketch of ∆ ABC and mark the given dimensions. C
Steps of Construction: 4.8 cm

1. Draw a line segment AB of 5.1 cm. A 5.1 cm B 60°
2. Construct ∠BAX = 60º (Fig. 1). A 5.1 cm B
3. Draw an arc of radius 4.8 cm taking A as centre which cuts AX at C (Fig. 2).

X X
C

4.8 cm

60° 60°
A 5.1 cm B A 5.1 cm B

Fig. 1 Fig. 2
C

4. Join BC. 4.8 cm
5. ABC is the required triangle.

60°
A 5.1 cm B

201