Question

(a) In the given figure, the base of the triangle is parallel to line $l$ and $\angle 1=\angle 2$. Prove that line BC & $m$ are parallel to each other.

(b) Consider the following figure. Find the angle y.

[4 MARKS]

Answer 1

(a) Steps: 1 Mark
Proof: 1 Mark
(b) Steps: 1 Mark
Correct Answer: 1 Mark

$\angle 1=\angle 2$ (given)
They are also corresponding angles.

$\Rightarrow l\parallel m...\left(i\right)$ (If corresponding angles are equal, then the lines are parallel)

Also, $l\parallel BC....\left(ii\right)$

From (i) and (ii):

$m\parallel l\parallel BC$.

$\Rightarrow m\parallel BC$.


(b) In $\Delta BDA$, x + x + y = ${180}^{\circ }$ (by angle sum property)
similarly, in $\Delta BDC$, x + x + $\angle BDC$ = ${180}^{\circ }$
Comparing the two equations, we have $\angle BDC$ = y.
Also, $\angle BDC$ + $\angle BDA$ = ${180}^{\circ }$ (linear pair)
or, y + y = ${180}^{\circ }$
or, y = ${90}^{\circ }$