Coordinates and moving shapes · Usually met around P4
Congruent shapes
Congruent: one fits exactly on the other.
How to do it
Method
Congruent: one fits exactly on the other
A 2 × 3 rectangle turned 90° is 3 × 2: still congruent
Another way
Trace and compare
Trace it, turn and flip it: if it fits, they're congruent
In full
Two shapes are congruent when they are exactly the same shape and size: trace one, and by sliding, flipping or turning it you can lay it exactly on the other. So a shape after a translation, reflection or rotation is congruent to the original. Congruent shapes have matching sides the same length, matching angles the same size, and the same area and perimeter. The same area alone (a 2 × 6 and a 3 × 4 rectangle) doesn't make shapes congruent; an enlarged or stretched shape isn't congruent. To check, count the squares along each side and see if they pair up; or trace it, turn and flip the tracing, and see if it fits.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Shapes P and Q are congruent.
True or false?
Show the answer and working
Answer: True
Turn Q round and see whether its sides by the right angle pair up with P's 2 and 1 squares.
Example 2
Shapes P and Q are congruent, and each square is 1 cm². What is the area of Q in cm²?
Show the answer and working
Answer: 6 cm²
Congruent shapes have the same area: P's sides by the right angle are 4 and 3, so its area is 4 × 3 ÷ 2 = 6.
Example 3
Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 5 cm, BC = 9 cm and CA = 6 cm. How long is EF in cm?
Show the answer and working
Answer: 9 cm
E matches B and F matches C, so EF matches BC: EF = 9 cm.
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