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AQA GCSE · Question 14.1 · Geometry and Measures
On the grid, draw a shape congruent to triangle A.
On the grid, draw a shape congruent to triangle A.
How to approach this question
1. **Understand "congruent":** Congruent means identical in shape and size. The new shape can be rotated or reflected (flipped), but its side lengths and angles must be the same as triangle A.
2. **Analyse Triangle A:** Look at its dimensions. It is a right-angled triangle. Its base is 3 units long (from x=2 to x=5 on the grid). Its height is 2 units long (from y=2 to y=4).
3. **Draw the new shape:** Pick a starting point on the grid and draw a triangle with a base of 3 units and a height of 2 units. It can be in any orientation. For example, you could draw it with vertices at (6,6), (9,6), and (6,8).
Full Answer
A triangle with the same dimensions as A (base 3, height 2) drawn anywhere on the grid, in any orientation.
The word "congruent" means that two shapes are identical in size and shape. All corresponding sides must have the same length, and all corresponding angles must be the same. The shape can be translated (moved), rotated (turned), or reflected (flipped) and still be congruent.
Triangle A is a right-angled triangle. We can measure its sides by counting the squares on the grid.
- The horizontal side (base) has a length of 3 units.
- The vertical side (height) has a length of 2 units.
To draw a congruent shape, we just need to draw another triangle with a base of 3 and a height of 2 anywhere else on the grid. The orientation does not matter.
Common mistakes
✗ Drawing a shape that is larger or smaller (this would be a similarity transformation, not congruence).\n✗ Drawing a shape with different side lengths (e.g., base 2, height 3).
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