Angles (Including Parallel Lines): WJEC GCSE Higher November 2023 Unit 1 Q15

Higher November 2023 Unit 1 Q15

WJECHigherCurrent spec2 marksAngles (Including Parallel Lines)Similar Shapes

15. In the following diagram:

\(CB\) and \(DE\) are parallel
\(CE\) and \(BD\) are straight lines
\(CA = AE\).

Prove that triangles \(ABC\) and \(ADE\) are congruent.
You must show all your working and explain your reasoning. [2]

Lines CE and BD cross at A; CB parallel to DE; CA = AE marked; angle BCA = 27°, angle DAE = 79°

Diagram not drawn to scale

Mark scheme

Scheme

Marks

Comments

Formally identifying (in writing) two appropriate pairs of equal angles
e.g. BAC = DAE and BCA = DEA (CA = AE given)
or BAC = 79˚ and DEA = 27˚ (CA = AE given)
AND
Explanation that the triangles are congruent due to angle, side, angle or ASA or equivalent.

(Check diagram)
If all three angles are used, they must all be correct.
For reference:

BAC = DAE = 79° (vertically opposite angles)

BCA = DEA = 27° (alternate angles)

ABC = ADE = 74° (angles in a triangle with alternate angles)

Award E1 for one of the following:

formally identifying at least one correct pair of angles
AND
explanation that the triangles are congruent due to angle, side, angle or ASA or equivalent.

a correctly completed diagram (at least two pairs of angles)
AND
Explanation that the triangles are congruent due to angle, side, angle or ASA or equivalent.

formally identifying (in writing) two pairs of matching angles (with no incorrect angles)
e.g. BAC = DAE and BCA = DEA (CA = AE given)
or BAC = 79˚ and DEA = 27˚ (CA = AE given)