Angles (Including Parallel Lines): Eduqas GCSE Foundation November 2024 Paper 1 Q25

Foundation November 2024 Paper 1 Q25

25.

(a)

Four triangles are shown in the diagram below.

Diagram not drawn to scale

For each of the following statements choose ‘True’, ‘False’ or ‘Need more information’.
Tick one box for each statement. [2]

Statement	True	False	Need more information
Triangle A is congruent to Triangle B
Triangle C is congruent to Triangle D
Triangle A is congruent to Triangle C

(b)

Is it possible to draw an isosceles triangle with an exterior angle of 60°?
Tick the appropriate box and show working to explain your reason. [2]

Yes ☐ No ☐

(c)

Two triangles are shown in the diagram below.

Diagram not drawn to scale

Show that the two triangles are mathematically similar. [2]

Scheme	Marks	Comments
Yes indicated or clearly implied (with indication of one 120° angle) with two 30° angles.	B2	B1 for a clear indication of interior angle of 120°

Mark scheme (c)

Scheme	Marks	Comments
(\(\frac{10}{7.5} = \frac{12}{9} = \frac{8}{6}\)) same scale factor = \(\frac{4}{3}\) oe OR (\(\frac{7.5}{10} = \frac{9}{12} = \frac{6}{8}\)) same scale factor = \(\frac{3}{4}\) oe	B2	B1 just for \(\frac{10}{7.5} = \frac{12}{9} = \frac{8}{6}\) OR \(\frac{7.5}{10} = \frac{9}{12} = \frac{6}{8}\) Award no marks if the ratios of less than three pairs of sides compared.
	(6)

Alternative method 1

Scheme	Marks	Comments
12:10:8 and 9:7·5:6 both simplify to 6:5:4 oe OR both equivalent to 108:90:72 oe	B2	B1 for stating 12:10:8 = 9:7·5:6 without simplifying to 6:5:4

Alternative method 2

Scheme	Marks	Comments
B2 for any one of the following: 7.5 × \(\frac{12}{9}\) = 10 AND 6 × \(\frac{12}{9}\) = 8 10 ÷ \(\frac{12}{9}\) = 7.5 AND 8 ÷ \(\frac{12}{9}\) = 6 9 × \(\frac{10}{7{\cdot}5}\) = 12 AND 6 × \(\frac{10}{7{\cdot}5}\) = 8 12 ÷ \(\frac{10}{7{\cdot}5}\) = 9 AND 8 ÷ \(\frac{10}{7{\cdot}5}\) = 6 9 × \(\frac{8}{6}\) = 12 AND 7·5 × \(\frac{8}{6}\) = 10 12 ÷ \(\frac{8}{6}\) = 9 AND 10 ÷ \(\frac{8}{6}\) = 7·5	B2	B1 for any one of the following: 7.5 × \(\frac{12}{9}\) = 10 OR 6 × \(\frac{12}{9}\) = 8 10 ÷ \(\frac{12}{9}\) = 7.5 OR 8 ÷ \(\frac{12}{9}\) = 6 9 × \(\frac{10}{7{\cdot}5}\) = 12 OR 6 × \(\frac{10}{7{\cdot}5}\) = 8 12 ÷ \(\frac{10}{7{\cdot}5}\) = 9 OR 8 ÷ \(\frac{10}{7{\cdot}5}\) = 6 9 × \(\frac{8}{6}\) = 12 OR 7·5 × \(\frac{8}{6}\) = 10 12 ÷ \(\frac{8}{6}\) = 9 OR 10 ÷ \(\frac{8}{6}\) = 7·5

Corrected by Westie's Workshop

The board's mark scheme printed “8 ÷ 12/9 = = 6” and “9 × 10/7·5 = = 12”. Changed to “8 ÷ 12/9 = 6” and “9 × 10/7·5 = 12” because the equals sign was printed twice by mistake (in both the B2 and B1 lists). Our text already showed a single “=”.

Original: see the board's mark scheme PDF (link above).