in the fig cd is the angle bisector of angle c , angle b = angle ace . Prove that angle adc = angle acd
1
djchamp007
14.02.2018
Math
Secondary School
+6?pts
Answered
In the figure CD is the angle bisector of angle C, angle B = angle ACE. Prove that angle ADC = angle ACD
?
2
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deepanshusingh1?
?
Helping Hand
Ad is equal to ac (isoceles triangle's equal sides)
So if sides of isosceles triangle are equal so angles are also equal so angle ADC is equal to angle ACD
Hence proved
2.8
54 votes
THANKS?44
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bhagyashreechowdhury?
?
Ace
Given:
CD is the bisector of angle C
Angle B = Angle ACE
To find:
Prove that angle ADC = angle ACD
Solution:
In ?BCD, we have
?BCD + ?BDC + ?DBC = 180? ....... [Angle sum property] .... (i)
Also, ?ADC + ?BDC = 180? ..... [Linear Pair] ...... (ii)
From equation (i) & (ii), we get
?BCD + ?BDC + ?DBC = ?ADC + ?BDC
? ?BCD + ?BDC + ?DBC - ?BDC = ?ADC
???BCD + ?DBC = ?ADC?............... (iii)
Now, according to the question we have,
?ABC = ?ACE ...... (iv)
and
?BCD = ?ECD ?.... [? CD is the bisector of angle C as given in the figure]...(v)
On adding eq. (iv) & (v), we get
?ABC + ?BCD = ?ACE + ?ECD
???ABC + ?BCD = ?ACD?...... (vi)
On comparing eq. (iii) & (vi), we get
??ADC = ??ACD
Hence proved
djchamp007
14.02.2018
Math
Secondary School
+6?pts
Answered
In the figure CD is the angle bisector of angle C, angle B = angle ACE. Prove that angle ADC = angle ACD
?
2
SEE ANSWERS
Log in?to add comment
Answers
?
deepanshusingh1?
?
Helping Hand
Ad is equal to ac (isoceles triangle's equal sides)
So if sides of isosceles triangle are equal so angles are also equal so angle ADC is equal to angle ACD
Hence proved
2.8
54 votes
THANKS?44
Comments?
?
Report
bhagyashreechowdhury?
?
Ace
Given:
CD is the bisector of angle C
Angle B = Angle ACE
To find:
Prove that angle ADC = angle ACD
Solution:
In ?BCD, we have
?BCD + ?BDC + ?DBC = 180? ....... [Angle sum property] .... (i)
Also, ?ADC + ?BDC = 180? ..... [Linear Pair] ...... (ii)
From equation (i) & (ii), we get
?BCD + ?BDC + ?DBC = ?ADC + ?BDC
? ?BCD + ?BDC + ?DBC - ?BDC = ?ADC
???BCD + ?DBC = ?ADC?............... (iii)
Now, according to the question we have,
?ABC = ?ACE ...... (iv)
and
?BCD = ?ECD ?.... [? CD is the bisector of angle C as given in the figure]...(v)
On adding eq. (iv) & (v), we get
?ABC + ?BCD = ?ACE + ?ECD
???ABC + ?BCD = ?ACD?...... (vi)
On comparing eq. (iii) & (vi), we get
??ADC = ??ACD
Hence proved