Question

please answer question number 14 and 15 as fast as possible

Answer 1

HEY MATE HERE IS UR ANSWER
GIVEN THAT ➡️ D AND E IS POINT ON BC OF TRIANGLE ABC SUCH THAT BD = EC AND AD = AE

WE NEED TO PROVE THAT

TRIANGLE ABD CONGRUENT TO ACE

PROOF ➡️

NOW IN TRIANGLE ABD AND ACE

WE KNOW THAT

AD = AE ( GIVEN ) ------ EQ (1)

BD = EC ( GIVEN ) ------- EQ (2)

NOW IN TRIANGLE ADE

AD = AE

BUT WE KNOW THAT OPPOSITE ANGLES OF EQUAL SIDES OF TRIANGLE ARE EQUAL .

THEREFORE

ANGLE ADE = ANGLE AED. ------ EQ (3)

NOW WE ALSO KNOW THAT

ANGLE ADB + ANGLE ADE = 180 ° ( LINEAR PAIR ) ----- (4)

AND SIMILARLY

ANGLE AEC + ANGLE AED = 180° ( LINEAR PAIR ) ------. (5)

FROM EQUATIONS (3) (4) AND (5) WE HAVE

ANGLE ADB = ANGLE AEC . -- (6)

NOW COMING BACK TO TRIANGLE ABD AND ACE

WE HAVE

AD = AE ( GIVEN)

BD = EC ( GIVEN )

AND

ANGLE ADB = AEC ( PROVED ABOVE IN EQ 6 )

NOW BY USING SAS CONGRUENCE RULE WE HAVE

TRIANGLE

ABD = ACE

HENCE PROVED .......

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