In the figure below, triangle $ABC$ is an isosceles triangle, where $AB=AC$. $BD$ is the

Question

In the figure below, triangle $ABC$ is an isosceles triangle, where $AB=AC$. $BD$ is the bisector of $\angle ABC$, i.e., $\angle ABD=\angle CBD$, and $BD$ intersects $AC$ at $E$. Given that $\angle BAC={{36}^{\circ }}$, $\angle BDC={{36}^{\circ }}$, find the sizes of $\angle ACB$, $\angle ABD$, $\angle BEC$. Hence, find the relationship between straight lines $AB$ and $CD$. Find all other isosceles triangle(s) in the figure, besides triangle $ABC$.

Accepted Answer

(i) ${72}^{\circ }$ (ii) ${36}^{\circ }$ (iii) ${72}^{\circ }$ (iv) $AB//CD$ (v) triangle $ABE$, triangle $BCE$, triangle $ECD$, triangle $BCD$

IP1U11 HOT Q1

IP1U11 HOT Q1

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