Mathematics

Name the types of the following triangles:

(i) ΔABC with AB = 8 cm, AC = 7 cm and BC = 5.5 cm.

(ii) ΔPQR with PQ = RP = 5 cm and QR = 7.3 cm.

(iii) ΔDEF with ∠D = 90°.

(iv) ΔXYZ with ∠Y = 90° and XY = YZ.

(v) ΔLMN with ∠L = 30°, ∠M = 70° and ∠N = 80°.

Triangles

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Answer

(i) In ΔABC, AB = 8 cm, AC = 7 cm and BC = 5.5 cm.

Since all three sides are different,

∴ ΔABC is a scalene triangle.

(ii) In ΔPQR, PQ = RP = 5 cm and QR = 7.3 cm.

Since two sides (PQ and RP) are equal,

∴ ΔPQR is an isosceles triangle.

(iii) In ΔDEF, ∠D = 90°.

Since one angle is a right angle,

∴ ΔDEF is a right-angled triangle.

(iv) In ΔXYZ, ∠Y = 90° and XY = YZ.

Since one angle is a right angle and two sides are equal,

∴ ΔXYZ is an isosceles right-angled triangle.

(v) In ΔLMN, ∠L = 30°, ∠M = 70° and ∠N = 80°.

Since all three angles are less than 90° (all acute), and all are different,

∴ ΔLMN is an acute-angled triangle.

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