In the roof truss shown, AB = 8 and m/_HAF = 37^(circ). Find: m/_BAD. (HINT: The design of the roof truss displays line symmetry.) 12210203661.jpg

Find the value of ${\displaystyle m\mathrm{\angle }BAD}$.
Use transitive property of congruence.
${\displaystyle \mathrm{△}ABD\stackrel{\sim }{=}\mathrm{△}AHF,m\mathrm{\angle }BAD\text{and}m\mathrm{\angle }HAF}$ are the angles of congruent triangles, ${\displaystyle m\mathrm{\angle }BAD=m\mathrm{\angle }HAF}$.
Substitute ${\displaystyle m\mathrm{\angle }HAF={37}^{\circ }\in m\mathrm{\angle }BAD=m\mathrm{\angle }HAF}$.
${\displaystyle m\mathrm{\angle }BAD={37}^{\circ }}$
Therefore, the value of ${\displaystyle m\mathrm{\angle }BADis{37}^{\circ }}$.