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Question
In each of the examples given below, a pair of triangles is shown. Equal parts of triangles in each pair are marked with the same signs. Observe the figures and state the test by which the triangles in each pair are congruent.
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Solution
(i)From the figure , we know that the three sides of ABC are equal to the three sides of PQR.
By SSS test, ABC ≅ PQR
(ii)From the figure , we know that the two sides and the included angle of XYZ are equal to the two sides and the included angle of LMN.
By SAS test, XYZ ≅ LMN.
(iii) From the figure , we know that the two angles and the included side of PRQ are equal to the two angles and the included side of STU.
By ASA test, PRQ ≅ STU.
(iv) From the figure , we know that the right angles ,hypotenuse and a side of LMN are equal to the right angle, hypotenuse and a side of PTR.
By Hypotenuse side test, LMN ≅ PTR.
By SSS test, ABC ≅ PQR
(ii)From the figure , we know that the two sides and the included angle of XYZ are equal to the two sides and the included angle of LMN.
By SAS test, XYZ ≅ LMN.
(iii) From the figure , we know that the two angles and the included side of PRQ are equal to the two angles and the included side of STU.
By ASA test, PRQ ≅ STU.
(iv) From the figure , we know that the right angles ,hypotenuse and a side of LMN are equal to the right angle, hypotenuse and a side of PTR.
By Hypotenuse side test, LMN ≅ PTR.
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