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NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.3 β Part 2
Right Angle-Hypotenuse-Side (RHS)
Theorem: Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and the corresponding side of the other triangle.
Q-2 AD is an altitude of an isosceles triangle ABC in which Show that
- AD bisects BC
- AD bisects .
Solution:
Given,
AD is an altitude of isosceles triangle ABC and
- In
and
,
(Given)
(Common)
Therefore, by RHS congruence condition.
Now,
(by CPCT)
Thus, AD bisects BC
- (by Corresponding Parts of Congruent Triangles) Thus, AD bisects
Q-3 Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of (see Fig) . Show that:
Solution:
Given, Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of
and
- and (AM and PN are medians)
also,
In and ,
(Given)
(Given)
(Proved above)
Therefore, by SSS congruence condition.
- In and ,
(Given)
(by Corresponding Parts of Congruent Triangles)
(Given)
Therefore, by Side- Angle-Side congruence condition.