Congruent is zoom ×1
Every congruent pair is similar, but not every similar pair is congruent.
Same shape and same size
In Class IX you learnt that two figures are congruent if they have the same shape and the same size.
Two circles with the same radius are congruent. Two circles with different radii are not.
Are two congruent figures also similar?
What this lesson covers
The idea
All congruent figures are similar, but similar figures need not be congruent.
Same shape and same size
In Class IX you learnt that two figures are congruent if they have the same shape and the same size.
Two circles with the same radius are congruent. Two circles with different radii are not.
Are two congruent figures also similar?
- Yes, always
- No, never
- Only sometimes
Sort the pairs
Turn the zoom dial to see where each blue figure fits. Then say what kind of pair it is.
Congruent is a special kind of similar
All congruent figures are similar, but similar figures need not be congruent.
Congruent figures fit with a zoom of ×1. A zoom of ×1 is still a zoom, so they are similar. Similar figures that fit at another zoom, like ×2, are not congruent.
Notes
All congruent figures are similar, but similar figures need not be congruent. Congruent means similar with a zoom of ×1.
Check yourself
Two squares each have side 5 cm. Which statement is true?
A circle of radius 3 cm and a circle of radius 5 cm are...
Two triangles are congruent. By what number must you zoom one of them to make it fit exactly on the other?
Answer: 1
Same shape and same size, so they fit with a zoom of ×1.
Which statement is true?
- They are similar but not congruent.. They have the same size too: they fit at ×1. That makes them congruent.
- They are similar and congruent. — correct. Yes! The same shape and the same size.
- They are congruent but not similar.. Congruent figures are always similar. At ×1 they also have the same shape.
- congruent.. Congruent figures have the same size. These radii are different.
- similar but not congruent. — correct. Yes! All circles are similar. These two have different sizes, so they are not congruent.
- not similar.. All circles are similar: zoom the small one by 5/3 and it fits the big one.
- Every similar pair is a congruent pair.. No. Circles of radius 1 cm and 2 cm are similar but not congruent.
- Congruent pairs and similar pairs have nothing in common.. Congruent pairs are a special kind of similar pairs: the zoom is ×1.
- Every congruent pair is a similar pair. — correct. Yes! A congruent pair fits at ×1, so it is similar.