Question
In the figure, AB = AC, 
= 48° and 
= 18° . Then
- BC > CD
- BC = CD
- BC < CD
- Cannot decide
Hint:
find out all the angles of the triangle BCD and check whether the properties match.
The correct answer is: BC = CD
BC = CD
Given AB= AC. This means that ABC is an isosceles triangle. <A = 48 degree. This means that sum of \
<B+ < C = 180 – 48 = 132 degree.
Since base angles of an isosceles triangle are equal, <B = < C = 132 / 2 = 66 degree.
Now, <ACD = 18 degree. => <BCD = 66 – 18 = 48 degree.
In triangle BCD, <BDC = 180- <DBC - < BCD = 180 – 66 – 48 = 66 degree.=<DBC
Therefore, triangle BCD is an isosceles triangle with BC = CD
an isosceles triangle is one that has two of its sides equal and the base angles equal to each other.
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