Download SSM L2 Unit 6

Yr 10 Unit 6 –Shape, Space and Measure – Higher - Similarity and
Congruence
5 lessons
Support Objectives
1 Match one side and one angle of congruent triangles, given some
dimensions.
Grade
C
Ref
Grade
Ref
AQA Higher book II pages 151 - 154
Core Objectives
1 Match sides and angles of similar triangles, given some
dimensions.
B
AQA Higher book II pages 151 - 154
2 Prove that two triangles are congruent.
A
AQA Higher book II pages 160 - 162
3 Prove the construction theorems.
A
AQA Higher book II pages 160 - 162
4 Find the area of a 2 – D shape, given the area of a similar shape
and the ratio.
A
AQA Higher book II pages 157 - 158
5 Find the volume of a 3 – D sold, given the volume of a similar solid
and the ratio.
A
AQA Higher book II pages 157 - 158
Extension Objectives
1 Solve more difficult vector geometry problems.
Grade
A*
Ref
AQA Higher book II page 162
2
Student Self Assessment Sheet
Objectives
Grade
1
2
3
4
5
6
7
Match one side and one angle of congruent
triangles, given some dimensions.
Match sides and angles of similar triangles, given
some dimensions.
Prove that two triangles are congruent.
Prove the construction theorems.
Find the area of a 2 – D shape, given the area of a
similar shape and the ratio.
Find the volume of a 3 – D sold, given the volume of
a similar solid and the ratio.
Solve more difficult vector geometry problems.
Vocabulary
C
B
A
A
A
A
A*
  
Opposite angles
Corresponding angles
Alternate angles
Ratio
Similar
Congruent
Ideas for starters
1) Revise ratios, simplifying, the link with fractions, unitary ratios, scale factors etc.
2) Give students a pair of equivalent ratios with one number missing. Get students to identify
the missing number.
3) Ask students to think of real-life examples of 2 –D and 3 –D shapes.
4) Ask students to complete the following prediction questionnaire:
* Similar triangles have the same shape
Always / sometimes / never
* Equilateral triangles are similar
Always / sometimes / never
* Isosceles triangles are similar
Always / sometimes / never
* Squares are similar
Always / sometimes / never
* Circles are similar
Always / sometimes / never
* Rectangles are similar
Always / sometimes / never
* Rhombuses are similar
Always / sometimes / never
* Parallelograms are similar
Always / sometimes / never
* Pentagons are similar
Always / sometimes / never
* Spheres are similar
Always / sometimes / never
* Cubes are similar
Always / sometimes / never
* Cuboids are similar
Always / sometimes / never
* Cylinders are similar
Always / sometimes / never
* Pyramids are similar
Always / sometimes / never
* Cones are similar
Always / sometimes / never
* Tetrahedra are similar
Always / sometimes / never
4) Ask students to draw a triangle with sides measuring 12cm, 10.5cm and 9cm. How many
triangles with sides 4cm, 3.5cm and 3cm can fit into it? What is the ratio of their sides?
What is the ratio of their areas?
Repeat for different shapes and 3 – D shapes.
5) Ask students to fill out a questionnaire about similarity and congruence:
* Similar figures are congruent
Always / sometimes /
* Congruent figures are similar
Always / sometimes /
* If the corresponding sides of two
Always / sometimes /
triangles are in the same ratio then
the triangles are congruent
* If two triangles are congruent
Always / sometimes /
then their corresponding angles
are equal
* If their corresponding angles are
Always / sometimes /
equal then two triangles are congruent
* If two shapes are congruent then
Always / sometimes /
they have the same area
never
never
never
never
never
never
* If two shapes have the same area then
they are congruent
* If two solids are congruent then they
have the same volume
* If two solids have the same volume then
they are congruent
Always / sometimes / never
Always / sometimes / never
Always / sometimes / never
6) Split the students into small groups; give each group an envelope containing six folded
pieces of paper with the following measurements written, one on each:
AB = 10cm, AC = 4cm, BC = 7cm, angle A = 320, angle B = 180, angle C = 1300
Ask the groups to choose three pieces of paper at random and draw the triangle based on the
information they have picked.
Put the pieces back in and repeat the experiment.
Students decide which information they need to produce congruent triangles.
HOLS/maths investigations
ICT links / citizenship
Ideas for Plenaries
1) Triangles are similar if their corresponding angles are equal. Is the same true of
quadrilaterals? Ask everyone to draw a quadrilateral with angles A = 700, B = 400, C = 1000
and D = 1500. Compare results.
2) Triangles are similar if their corresponding sides are in the same ratio. Is the same true
of all quadrilaterals?
3) Do the similarity / congruence questionnaires.
4) Bring in pairs of objects, some of which are similar and some are not. Discuss the
properties of the similar shapes.
5) Imagine an architect’s scale model of a real house; the ratio of corresponding lengths is
1 : 20. Discuss the following:
What is the ratio of the height of the model to the height of the house?
Also consider:
Width
Number of rooms
Area of kitchen floor
Capacity of bath tub
Number of stairs
Paint on the front door
Glass in the windows
Space in the loft
6) Ask students to draw:
a) Two rectangles that are congruent
b) Two rectangles that are similar but not congruent
c) Two rectangles that are not similar
d) Two rectangles that are congruent but not similar
Ideas for homework
1) AQA Higher homework book II pages 61 - 62 homework 1.
2) AQA Higher homework book II page 63 homework 2.
3) AQA Higher homework book II page 64 homework 3.
Webmaths – similar shapes
Ideas for Formative Comments