Question

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subject : maths

class : 10th

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Answer 1

★ Question:

∆ABC ≅ ∆ZXY. State whether the following statements are true or false.

(i) AB = XY

(ii) If ∠B = 30°, ∠X = 30°

(iii) If ∠Z = 70° and ∠X = 30°, find the measure of ∠C

Answer:

1. False
2. True
3. 80°

Step-by-step explanation:

When 2 triangles are said to be congruent, their corresponding sides would be equal.

Here ∆ABC ≅ ∆ZXY. So,

• AB = ZX
• BC = XY
• AC = ZY
• ∠A = ∠Z
• ∠B = ∠X
• ∠C = ∠Y

From the above correspondence, we can understand that AB ≠ XY. So, first statement is False.

For second part of the question

Also, ∠B = ∠X.

So if ∠B = 30° then ∠X will also be 30°.

For third part of the question:

In ∆ ZXY, by Angle Sum Property;

∠Z + ∠X + ∠Y = 180°

⇒ ∠Z + ∠X + ∠C = 180° (∵ ∠Y = ∠C)

⇒ 70° + 30° + ∠C = 180°

⇒ ∠C = 180° - 100°

⇒ ∠C = 80°

∴ ∠C = 80°