Question

Teacher has asked the children to construct a triangle with angles $60 °, 40 °$ and with a side $5 cm$ . Sushma calculated the third angle of the triangle as $80 °$ using angle - sum property of triangle. Then Kamal, Sushma and Namratha constructed triangles differently using the following measurements.

Kamal: $60 °, 40 °$ and $5 cm$ side (as teacher said)

Sushma: $80 °, 40 °$ and $5 cm$ side

Namratha: $60 °, 80 °$ and $5 cm$ side.

They cut these triangles and place them one upon the other. Are all of them congruent? Justify.

Accepted Answer

Given,

The dimensions of the triangle $1$ drawn by Kamal: $60 °, 5 cm, 40 °$

The dimensions of the triangle $2$ drawn by Sushma: $80 °, 5 cm, 40 °$

The dimensions of the triangle $3$ drawn by Namratha: $60 °, 5 cm, 80 °$

Now, we can compare two triangles by $5 cm$ congruence criterion.

According to $A S A$ congruence criterion, two triangles are congruent if two pairs of angles and one pair of corresponding included sides are equal.

In triangles $1 & 2$ , $60 ° \neq 80 °$

In triangles $2 & 3$ , $40 ° \neq 60 °$

In triangles $1 & 3$ , $40 ° \neq 80 °$

Therefore, all three triangles are not congruent with each other.

Telangana Board Solutions for Chapter: Congruency of Triangles, Exercise 5: Try This

Telangana Board Mathematics Solutions for Exercise - Telangana Board Solutions for Chapter: Congruency of Triangles, Exercise 5: Try This

Questions from Telangana Board Solutions for Chapter: Congruency of Triangles, Exercise 5: Try This with Hints & Solutions

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