Question

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
(i) AD bisects BC
(ii) AD bisects Z A.​

Answer 1

PROVING :

• TRAINGLE ABC IS AN ISOSCELES TRIANGLE

• AB = AC .....(I)

• ALSO, AD IS THE ALTITUDE

• SO, ANGLE ADC = ANGLE ADB = 90° ...(2)

• IN TRIANGLE ADB AND TRIANGLE ADC

• ANGLE ADC = ANGLE ADB = 90° ( BOTH 90°)

• AB = AC (FROM 1)

• AD= AD( COMMON)

• SO , PROVED CONGRUENT BY RHS CONGRUENCY

MORE:

• RHS congruence theorem states that, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, the two triangles are congruent. This rule is only applicable in right-angled triangles.