Question

12. In the AABC, AB = AC and ABAD=ACAD SHOW THAT
(a) ABAD = ACAD
(b) BD = CD
(c) ZADB = ZADC =​

Answer 1

Given

AB =AC....... 1

angle BAD =angle CAD.........2

in ∆BAD & ∆CAD

AB = AC........ given(1)

angle BAD =angle CAD...... given (2)

AD = AD......... common

hence

∆BAD is congruent to ∆ CAD

by SAS congruent rule.

a) angle BAD is congruent to angle CAD

.......[ by C. P. C. T]

b) BD =CD .......[ by C. P. C. T]

c)

angle ADB= angle ADC .......[ by C. P. C. T]..... 3

angle ADB + angle ADC =180°........ 4

( angel sum property of a linear line)

from 3

angle ADB= angle ADC

therefore

angle ADB + angle ADB =180°

2 * angle ADB =180°

angle ADB =90°

put in eq 4

angle ADB + angle ADC =180°

90° + angle ADC =180°

angle ADC = 90°

hence

angle ADB= angle ADC=90°