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Home , Isosceles triangle, Rectangle

1 A shaded isosceles is drawn inside a .

Calculate the size of a.

2 marks

2 The following all have a of 36 cm.

Here is a table to show the of each side.

Complete the table.

One is done for you.

Side

9 cm 9 cm 9 cm 9 cm

rectangle 3 cm

9 cm

10 cm

2 marks

St+Philip%27s+CE+Primary+School Page 1 of 14

3 Here is a on a grid.

For each statement, put a tick (✔) if it is true. Put a cross (✘) if it is not true.

The shape is a quadrilateral.

The shape has 2 lines of .

The shape is a .

The shape has one .

2 marks

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4 Anna has four different .

Complete the table to show the size of the in each triangle.

Type of triangle Angle 1 Angle 2 Angle 3

Isosceles 90°

Right-angled 80°

Isosceles 70°

Isosceles 70°

2 marks

5 Here is a .

Draw two straight lines across the hexagon to make two triangles and two quadrilaterals.

1 mark

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6 Join dots on the grid to make a quadrilateral that has 3 acute angles.

1 mark

St+Philip%27s+CE+Primary+School Page 4 of 14

7 the with exactly four acute angles.

1 mark

St+Philip%27s+CE+Primary+School Page 5 of 14 Adam has this rectangular piece of card. It is marked with grid lines. 8

Adam makes two straight cuts along the grid lines.

The two cuts divide the rectangle into 3 :

• 2 of different size, and

• 1 rectangle.

Using the grid lines, draw two lines that show where Adam could have made his cuts.

Use a ruler. 1 mark

9 Look at the letters below.

Circle the letter below that has both and lines.

1 mark

10 A bicycle wheel has a of 64 cm.

What is the radius of the bicycle wheel?

1 mark

St+Philip%27s+CE+Primary+School Page 6 of 14 Two of the angles in a triangle are 70° and 40° 11 Jack says,

Explain why Jack is not correct.

1 mark

St+Philip%27s+CE+Primary+School Page 7 of 14 Here is a sketch of a triangle. 12 It is not drawn to scale.

Draw the full-size triangle accurately below.

Use an angle measurer (protractor) and a ruler.

One has been drawn for you.

2 marks

St+Philip%27s+CE+Primary+School Page 8 of 14 Mark schemes

Award TWO marks for the correct answer of 104°. 1 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g:

• 180 − 38 − 38 = a Answer need not be obtained for the award of ONE mark. Up to 2 [2]

Completes all three rows correctly, eg: 2 • rectangle 3cm 3cm 15cm 15cm

rhombus 9cm 9cm 9cm 9cm

kite 10cm 10cm 8cm 8cm

! Measures Accept Side lengths in each row may be given in any order Accept correct values with cm omitted eg, for the rectangle: • 15 3 15 2

or

Completes two rows correctly 1 [2]

Award TWO marks for all four boxes ticked or crossed correctly as shown: 3

St+Philip%27s+CE+Primary+School Page 9 of 14 If the answer is incorrect, award ONE mark for three boxes ticked or crossed correctly. Accept alternative unambiguous indications eg Y or N. For TWO marks accept:

Up to 2m [2]

Completes all four rows of the table correctly, eg: 4 90° 45° 45°

80° 90° 10°

70° 70° 40°

70° 55° 55°

Accept angles within a row in either order Accept the bottom two rows may be given in either order ! Condone omission of degree signs ! For 2 marks, do not accept correct angles in 3rd row repeated in 4th row, in either order 2

or

Completes three rows correctly 1 [2]

St+Philip%27s+CE+Primary+School Page 10 of 14 Diagram completed as shown: 5

OR

Accept slight inaccuracies in drawing, provided the intention is clear. Diagrams may be completed in any orientation. U1 [1]

A quadrilateral with three acute angles, e.g. 6

OR

St+Philip%27s+CE+Primary+School Page 11 of 14 OR

Accept inaccurate drawing provided the intention is clear. [1]

7 The correct shape circled as shown:

Accept alternative unambiguous positive indications, e.g. shape ticked. [1]

Rectangle divided, as shown: 8

St+Philip%27s+CE+Primary+School Page 12 of 14 OR

OR

OR

Accept slight inaccuracies in drawing provided the intention is clear. [1]

9 The correct letter circled as shown:

Accept alternative unambiguous positive indications, e.g. letter ticked. [1]

10 32 [1]

St+Philip%27s+CE+Primary+School Page 13 of 14 An explanation showing an understanding: 11 • that this specific triangle has angles 70, 70 and 40

OR

• of the properties of an − all angles are equal (60°)

and therefore that this triangle cannot be equilateral, e.g.

• The angles aren’t 60° • There is not a 60° angle • It has two different angles (70° and 40°) so it can’t be equilateral • The angles aren’t the same • An equilateral triangle has 60° + 60° + 60° • All the angles are the same in an equilateral triangle • It’s an .

(In the context of this question, the term isosceles triangle is treated as not including equilateral triangles as a special type, as the national curriculum does not specify this at key stage 2.) Do not accept vague or incomplete explanations, e.g. • The other angle is 70° • They aren’t (all) the same. (No reference to angles) • An equilateral triangle has equal angles. (Does not say all.) Do not accept explanations which include incorrect mathematics or incorrect information that is relevant to the explanation, e.g. • 40 + 70 = 110 + 70 = 180 [1]

Award TWO marks for a completed triangle that has all of the following three points: 12 • an angle in the range 33° to 37° inclusive for the angle marked 35° • an angle in the range 88° to 92° inclusive for the right angle • the triangle has been drawn on an 8cm line (either on the given line or a line drawn), provided they have constructed both angles within the tolerance of the line 7.9 cm to 8.1 cm.

If the answer is incorrect, award ONE mark for a completed triangle and TWO of the three points correct. Accept drawings where any side has been extended past a . When considering whether the triangle is completed, do not accept: • a quadrilateral or another shape drawn OR • a curved line that is used to complete the shape OR • sides not meeting to form a vertex. Up to 2m [2]

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