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

Question

In the figure below, the triangle $ABC$ is an isosceles triangle, where $AB = AC$. $BD$ is the bisector of angle $ABC$, i.e., angle $ABD = \text{angle}\hspace{0.5em} CBD$, and $BD$ intersects $AC$ at $E$. Given that angle $BAC = 36^\circ$ and $BDC = 36^\circ$, find the sizes of angle $ACB$, angle $ABD$, angle $BEC$. Hence deduce the relationship between line segments $AB$ and $CD$. Name all other isosceles triangle(s) in the figure other than triangle $ABC$.

Accepted Answer

(i) $72^\circ$ (ii) $36^\circ$ (iii) $72^\circ$ (iv) $AB\parallel CD$ (v) $\triangle ABE$, $\triangle BCD$, $\triangle BEC$, $\triangle ECD$

Angles Formed by Two Parallel Lines and a Transversal

Angles Formed by Two Parallel Lines and a Transversal

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