1MA0 Higher November 2013 Paper 2 Q28
*28
Diagram NOT accurately drawn
\(AOC\) and \(BOD\) are diameters of a circle, centre \(O\).
Prove that triangle \(ABD\) and triangle \(DCA\) are congruent. (3)
| Answer | Mark | Notes |
|---|---|---|
| Proof | 3 | M1 for one pair of equal angles or sides with reason M1 for second pair of equal angles or sides with reason C1 for proof completed correctly with full reasons and reason for congruence Acceptable reasons: \(AD\) common (oe eg both same) Angle \(BAD\) = angle \(CDA\) (angles in a semicircle are 90°) Angle \(ABO\) = angle \(DCA\) (angles in the same segment are equal) Triangle \(ABD\) and triangle \(DCA\) are congruent - ASA OR \(BD = CA\) (diameters of the circle) Angle \(BAD\) = angle \(CDA\) (angles in a semicircle are 90°.) \(AD\) common Triangle \(ABD\) and triangle \(DCA\) are congruent - RHS OR \(BD = CA\) (diameters of the circle) \(AD\) is common Angle \(ADB\) = angle \(CAD\) (base angles of an isosceles triangle are equal.) Triangle \(ABD\) and triangle \(DCA\) are congruent - SAS |