Question 14 Marks

In figure, AB || DC and AB = DC.

1. Is $\triangle\text{ACD}\cong\triangle\text{CAB}?$
2. State the three pairs of matching parts used to answer (i).
3. Which angle is equal to $\angle\text{CAD}?$
4. Does it follow from (iii) that AD || BC?

​​​​​​​​​​​​​​

Answer

1. Yes by SAS condition of congruency, $\triangle\text{DCA}\cong\triangle\text{BAC}$.
2. We have used AB = DC, AC = CA and $\angle\text{DCA}=\angle\text{BAC}$.
3. $\angle\text{CAD}=\angle\text{ACB}$ since the two triangles are congruent.
4. Yes this follows from AD || BC as alternate angles are equal. lf alternate angles are equal the lines are parallel.

View full question & answer→