Question

(a) Observe the given triangles and explain, why is $\Delta ABC\cong \Delta FED$?



(b) In a $\Delta$ABC, $\angle$B = 50${}^{\circ }$ and $\angle$C is 60${}^{\circ }$. Find $\angle$A.
[4 MARKS]

Answer 1

(a) Proof: 2 Marks

(b) Steps: 1 Mark
Final answer: 1 Mark

(a) In $\Delta ABC$ and $\Delta FED$,

$\angle B=\angle E={90}^{\circ }$ [Given]

$\angle A=\angle F$ [Given]

$BC=ED$ [Given]

$\Rightarrow$ Two angles and one side of $\Delta ABC$ are equal to two angles and one side of $\Delta FED$.

Therefore, $\Delta ABC\cong \Delta FED$ [AAS congruence rule]

(b) Sum of the angles of a triangle = 180${}^{\circ }$

$\angle$A + $\angle$B + $\angle$C = 180${}^{\circ }$

$\angle$A = 180${}^{\circ }$– (50${}^{\circ }$ + 60${}^{\circ }$) = 180${}^{\circ }$ – 110${}^{\circ }$ = 70${}^{\circ }$