Q1 of 24 Page 21

In each pair of triangles below, find matching pairs of sides and write their names.

In Δ LMN and Δ XYZ,

LN = XY = 8 cm


∠L = ∠Y = 30°


In Δ LMN, sum of all angles of triangle is 180°


∴ ∠L + ∠M + ∠N = 180°


30 + 80 + ∠N = 180


110 + ∠N = 180


∴ ∠N = 180-110


= 70°


Here, ∠N = ∠X = 70°


According to property,


If one side of a triangle and angle at its ends are equal to one side of another triangle and the angles at its ends, then the third angles are also equal and the sides opposite equal angle are equal.


{Here, LN and XY is the required side}


In Δ LMN and Δ XYZ,


NM is opposite ∠L and XZ is opposite ∠Y


Also, LM is opposite ∠N and YZ is opposite ∠X


∴ NM = XZ


And LM = YZ


Also, LN = XY = 8 cm (given)


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In each pair of triangles below, find matching pairs of sides and write their names.

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In the figure, AP and BQ equal and parallel are lines drawn at the ends of the line AB. The point of intersection of PQ and AB is marked as M.


i) Are the sides of Δ AMP equal to the sides of Δ BMQ? Why?


ii) What is special about the position of M on AB?


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i) Are the sides of Δ BPC equal to the sides of Δ EQD? Why?


ii) Are the side of AP and AQ of Δ APQ equal? Why?