Question

In adjacent figures
(i) State which three parts of triangleABC and triangleDEF are equal
(ii) Prove triangle ABC = triangle DEF
(iii) Find x​

Answer 1

STEP-BY-STEP EXPLANATION:

.

(i) State which three parts of ∆ABC and ∆DEF are equal.

∠BAC = ∠EDF •••[Shown In Figure]

∠ABC = ∠DEF •••[Shown In Figure]

BC = EF •••[Shown In Figure]

Therefore,

• ∠BAC = ∠EDF
• ∠ABC = ∠DEF
• BC = EF

(ii) Prove ∆ABC ≅ ∆DEF.

In ∆ABC,

∠ABC + ∠BCA + ∠CAB = 180° •••[ASPo∆]

• ➺ 70° + ∠BCA + 40° = 180°
• ➺ 110° + ∠BCA = 180°
• ➺ ∠BCA = 180° - 110°
• ➺ ∠BCA = 70° •••[1]

In ∆DEF,

∠DEF + ∠EFD + ∠FDE = 180° •••[ASPo∆]

• ➺ 70° + ∠EFD + 40° = 180°
• ➺ 110° + ∠EFD = 180°
• ➺ ∠EFD = 180° - 110°
• ➺ ∠EFD = 70°

By Eq [1],

• ➺ ∠EFD = ∠BCA •••[2]

In ∆ABC and ∆DEF,

• ∠ABC = ∠DEF = 70°
• BC = EF •••[given]
• ∠EFD = ∠BCA •••[2]

By ASA congruecy rule,

• ∆ABC ≅ ∆DEF

Hence Proved

(iii) Find x.

AC = DF •••[CPCT]

• ➺ (2x - 3) cm = (x + 4) cm
• ➺ 2x - 3 = x + 4
• ➺ 2x - x = 4 + 3
• ➺ x = 7

Hence,

• The value of x is 7.