“If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

Solution:

We know that

If the corresponding angles of two triangles are equal, from the angle sum property, the corresponding third angle will be equal.

So if two corresponding angles and sides are equal, then we can prove the triangles using the SAS criterion.

The SAS criterion states that If two sides of one triangle are respectively proportional to two corresponding sides of another, and if the included angles are equal, then the two triangles are congruent.

So both SAS and ASA are treated the same.

Therefore, the statement is true.

✦ Try This: Two sides of a triangle are of lengths 10 cm and 4.5 cm. The length of the third side of the triangle cannot be a. 3.6 cm, b. 4.1 cm, c. 5.4 cm, d. 3.4 cm

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7

NCERT Exemplar Class 9 Maths Exercise 7.2 Problem 4

“If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

Summary:

The statement “If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent” is true

☛ Related Questions:

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