Page 210 - Start Up Mathematics_7

Example 5: Construct ∆ DEF such that DE = 5 cm, DF = 3 cm and F
m∠EDF = 90°. 3 cm
Solution: Construction: Draw a rough sketch of ∆ DEF and mark
the given dimensions. 90°
Steps of Construction: D 5 cm E
1. Draw a line segment DE of 5 cm.
2. Construct ∠EDX = 90º (Fig. 1). D 5 cm E

X

D 5 cm E
Fig. 1
3. Draw an arc of radius 3 cm taking D as centre and cutting DX at F (Fig. 2).
X
F F

3 cm

3 cm

D 5 cm E D 5 cm E
Fig. 2 Fig. 3
4. Join EF.
5. DEF is the required triangle (Fig. 3).

Case III: ASA criterion
Construction of a triangle when two of its angles and an included side are given
Let’s construct a triangle ABC in which BC = 5.6 cm and ∠B = 60º and A
∠C = 45º.
Construction: Draw a rough sketch of ∆ ABC and mark the given dimensions.
Steps of Construction: 60° 45°
1. Draw a line segment BC of 5.6 cm. B 5.6 cm C B 5.6 cm C
2. Construct ∠CBX = 60º (Fig. 1).

Y X
X A

60° 60°
B 5.6 cm C B 5.6 cm C
Fig. 1 Fig. 2

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