Triangle ABC is an isosceles triangle with AB= BC. Prove that triangle ABC is congurent to triangle CBA
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It is given that two circle having radii 5.5 cm and 4.2 cm touch each other externally. We know, the distance between the centres of the circles touching externally is equal to the sum of their radii. Thus, the distance between their centres is 9.7 cm.
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In ∆ ABC
GIVEN= AB=BC
TO PROVE = ∆ABC IS CONGRUENT TO ∆ CBA
CONSTRUCTION= AD PERPENDICULAR BC
PROOF= IN ∆ABD AND ∆ADC
= AD= AD ( COMMON)
= AB= BC ( GIVEN)
= ANGLE ADB=ANGLE ADC ( EACH 90 DEGREE)
= SO ( ∆ABD CONGRUENT TO∆ADC) BY SAS
IF ∆ABD CONGRUENT TO ∆ADC THEREFORE ∆ ABC IS CONGRUENT TO ∆ CBA
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