In the figure if AC is bisector of angle BAD such that AB=3 cm and AC=5 cm, then What is CD equal to.
Answers
AC = AC
angle B = angle D
angle BAC = angle DAC
by AAS CRITERIA
triangle BAC is congurent to triangle DAC
by CPCT
AD = BC = 3 cm
in triangle ACD
(AC) ^ 2 = ( CD) ^2 + ( AD)^2
(5)^2 = (CD)^2 + ( 3)^2
25-9 = (CD) ^2
CD = √16 = 4 CM
Given : AB = 3 cm and AC = 5 cm
AC is bisector of angle BAD
To Find : CD
(a) 4 cm
(b) 2 cm
(c) 3 cm
(d) 5 cm
Solution:
ΔABC is right angle
Pythagoras theorem:
Square on the hypotenuse of a right-angled triangle is equal to the
sum of the squares of the other two perpendicular sides.
AC² = AB² + BC²
=> 5² = 3² + BC²
=> BC² = 4²
=> BC = 4 cm
in Δ ABC and ΔADC
∠BAC = ∠DAC as AC is bisector of angle BAD
∠ABC = ∠ADC = 90°
AC = AC common
=> ΔABC ≅ ΔADC using AAS congruence
Hence
BC = CD using corresponding parts of congruent triangles are equal
Hence , CD = 4 cm
Correct option is a) 4 cm
Learn More:
Solve a proportion to find the missing side. The figures are similar to ...
brainly.in/question/17153989
we know in a triangle sum of any two sides is greater than the third ...
brainly.in/question/6691141