Year 6 Maths: Congruent Shapes

What are Congruent Shapes?

Hello Year 6! Today, we are going to learn about congruent shapes. But what do we mean by “congruent”?

Congruent shapes are shapes that are exactly the same in size and shape. If you were to place one shape on top of the other, they would match perfectly.

Key Rules

1. Same Size: Congruent shapes have the same dimensions. This means if one shape is a triangle with sides that are 3 cm, 4 cm, and 5 cm, any congruent triangle must have those exact measurements.
2. Same Shape: The shapes must look the same. For example, a square is congruent to another square if they both have four equal sides.
3. Orientation Doesn’t Matter: Congruent shapes can be flipped or rotated, but they still match. Imagine a triangle turned upside down; it can still be congruent!

Examples

• Two squares that both have sides of 5 cm are congruent.
• Two circles that both have a radius of 2 cm are congruent.
• Two rectangles that are both 4 cm long and 2 cm wide are congruent.

Tips and Tricks

• Use a ruler: Measure the sides of the shapes to check if they are the same length.
• Use a compass: If you have two circles, you can use a compass to check if they have the same radius.
• Visuals: Sometimes, it helps to cut out shapes. If you can cut one shape and lay it over another, you can see if they are congruent.

Engaging Questions

1. Can you think of two objects around you that are congruent?
2. If I have a triangle with sides measuring 3 cm, 4 cm, and 5 cm, can you create another triangle that is congruent?

Questions on Congruent Shapes

Easy Level Questions

1. What does it mean for shapes to be congruent?
2. Are two circles with different sizes congruent? (Yes/No)
3. How many sides does a triangle have?
4. Can a square be congruent to a rectangle? (Yes/No)
5. If two rectangles have the same length and width, are they congruent? (Yes/No)
6. What shape is congruent to a square?
7. Are two triangles with the same angles but different side lengths congruent? (Yes/No)
8. What do you call shapes that are not congruent?
9. If you turn a square around, is it still congruent to itself? (Yes/No)
10. Can two shapes be congruent if one is bigger than the other? (Yes/No)
11. How many equal sides does an equilateral triangle have?
12. If I have a rectangle that is 5 cm by 3 cm, what dimensions must another rectangle have to be congruent?
13. Are two circles with the same radius congruent? (Yes/No)
14. How can you check if two shapes are congruent?
15. What shape is always congruent to itself?
16. If two triangles have sides measuring 5 cm, 12 cm, and 13 cm, are they congruent? (Yes/No)
17. What is one way to find congruent shapes?
18. If I have a hexagon with all sides equal, can you create a congruent hexagon? (Yes/No)
19. Can you give an example of two congruent objects at home?
20. If two shapes have the same area but different shapes, are they congruent? (Yes/No)

Medium Level Questions

1. What is the difference between congruent shapes and similar shapes?
2. How would you prove that two triangles are congruent?
3. If two pentagons have sides measuring 4 cm each, are they congruent? (Yes/No)
4. Can two shapes be congruent if they are different colours? (Yes/No)
5. If a rectangle has a length of 10 cm and a width of 5 cm, what dimensions would another rectangle need to be congruent?
6. Can two congruent circles be of different colours? (Yes/No)
7. If a shape has an area of 20 cm², can it be congruent to another shape with an area of 30 cm²? (Yes/No)
8. What do you call two shapes that are the same shape but different sizes?
9. What kind of triangles are always congruent if they have the same angles?
10. If I have a triangle with sides of 6 cm, 8 cm, and 10 cm, can you find another triangle that is congruent?
11. Can congruent shapes have different orientations? (Yes/No)
12. If two shapes are congruent, what can you say about their perimeters?
13. Can a congruent triangle be larger than another? (Yes/No)
14. Are two squares with sides of 1 m and 1 m congruent? (Yes/No)
15. If I flip a triangle, is it still congruent? (Yes/No)
16. Can two shapes be congruent in only one dimension? (Yes/No)
17. How many congruent angles does an equilateral triangle have?
18. If two shapes are congruent, what can you say about their corresponding sides?
19. What is a real-life example of congruent shapes?
20. If two circles have diameters of 6 cm and 12 cm, are they congruent? (Yes/No)

Hard Level Questions

1. Explain how you would show that two shapes are congruent using transformations.
2. What properties must two triangles share to be considered congruent?
3. If two shapes are similar but not congruent, what does that mean?
4. How would you determine if two irregular quadrilaterals are congruent?
5. What is the importance of congruence in real life? Give an example.
6. If two squares have areas of 16 cm² and 25 cm², are they congruent? (Yes/No)
7. Can you find congruent shapes using only angles? Explain how.
8. If I have a triangle with angles measuring 60°, 60°, and 60°, what can you say about another triangle with the same angles?
9. If two shapes have the same perimeter but are different shapes, are they congruent? (Yes/No)
10. How can you use tracing paper to check for congruence?
11. What happens to the congruence of shapes if one is stretched? (Explain)
12. If I have an isosceles triangle, can another isosceles triangle with different side lengths be congruent? (Yes/No)
13. Could you create a 3D model of congruent shapes? Give an example.
14. Are two trapeziums with the same area congruent? (Yes/No)
15. If you have a rectangle and a triangle, can they ever be congruent? (Yes/No)
16. Describe a process to find congruent shapes in nature.
17. Explain how congruence is used in architecture.
18. Can a shape have congruent parts that are not congruent to the whole? (Yes/No)
19. What role does symmetry play in congruence?
20. If two shapes are congruent, what can be said about their corresponding diagonals?

Answers to Questions

Easy Level Answers

1. Shapes that are the same size and shape.
2. No.
3. Three.
4. No.
5. Yes.
6. Another square.
7. No.
8. Non-congruent shapes.
9. Yes.
10. No.
11. Three.
12. 5 cm by 3 cm.
13. Yes.
14. Measure the sides or angles.
15. Yes.
16. Yes.
17. By cutting and overlaying.
18. Yes.
19. Yes.
20. No.

Medium Level Answers

1. Congruent shapes are the same size and shape, while similar shapes are the same shape but different sizes.
2. By measuring sides and angles or using transformations.
3. Yes.
4. No.
5. 10 cm and 5 cm.
6. Yes.
7. No.
8. Similar shapes.
9. Equilateral triangles.
10. Yes, the same sides.
11. Yes.
12. They are equal.
13. No.
14. Yes.
15. Yes.
16. No.
17. Three equal angles.
18. They must be equal.
19. Two paper cut-outs of the same shape.
20. No.

Hard Level Answers

1. By using rotations, reflections, and translations.
2. They must have equal corresponding sides and angles.
3. They are the same shape but different sizes.
4. Measure the sides and angles.
5. In construction, ensuring parts fit together.
6. No.
7. No, angles alone don’t determine congruence.
8. They are congruent.
9. No.
10. Yes, by tracing and matching.
11. They will not be congruent.
12. No.
13. Yes, for example, making two identical cubes.
14. No.
15. No.
16. By observing patterns.
17. It ensures structural integrity.
18. Yes.
19. It helps identify congruent shapes.
20. No.

Feel free to ask any questions or for further explanations! Happy learning!