It is given that ∆ ABC ≅ ∆ FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
a. DF = 5 cm, ∠F = 60°
b. DF = 5 cm, ∠E = 60°
c. DE = 5 cm, ∠E = 60°
d. DE = 5 cm, ∠D = 40°
Solution:
It is given that
∆ ABC ≅ ∆ FDE
AB = 5 cm
∠B = 40°
∠A = 80°
By c.p.c.t DF = AB
So DF = 5 cm
By c.p.c.t ∠E = ∠C
By angle sum property in ∆ ABC
∠A + ∠B + ∠C = 180°
By substituting the values
80° + 40° + ∠C = 180°
120° + ∠C = 180°
So we get
∠C = 180° - 120°
∠C = 60°
So ∠E = ∠C = 60°
Therefore, DF = 5 cm, ∠E = 60° is true.
✦ Try This: It is given that ∆ PQR ≅ ∆ ZXY and PQ = 4 cm, ∠Q = 30° and ∠P = 60°. Then which of the following is true? a. XZ = 4 cm, ∠Z = 90°, b. XZ = 4 cm, ∠Y = 90°, c. XY = 4 cm, ∠Y = 90°, d. XY = 4 cm, ∠X = 60°
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7
NCERT Exemplar Class 9 Maths Exercise 7.1 Problem 7
It is given that ∆ ABC ≅ ∆ FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?, a. DF = 5 cm, ∠F = 60° , b. DF = 5 cm, ∠E = 60° , c. DE = 5 cm, ∠E = 60° , d. DE = 5 cm, ∠D = 40°
Summary:
It is given that ∆ ABC ≅ ∆ FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. DF = 5 cm, ∠E = 60° is true
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