Discover what makes two figures congruent — exactly identical in shape and size — starting Part 2 of the book.
Two figures are congruent if one can be placed exactly on top of the other, matching perfectly — same shape and same size. This is different from figures that are merely similar (same shape, different size).
Two circles have the same radius. Are they congruent?
Yes, since all circles with equal radii are exactly the same size and shape
Two squares have sides 4cm and 6cm. Are they congruent?
No — even though both are squares, their different sizes mean they aren't congruent
Two triangles are congruent if all three corresponding sides and all three corresponding angles match exactly. Checking a few key measurements (like SSS — all three sides equal) is enough to confirm this without measuring everything.
Triangle ABC has sides 5cm, 6cm, 7cm. Triangle DEF has sides 5cm, 6cm, 7cm. Are they congruent?
Yes, by the SSS (Side-Side-Side) rule, since all three corresponding sides match
If two triangles are congruent, what can you say about their corresponding angles?
They must be exactly equal, since congruent shapes match perfectly in every way
1. Two rectangles both have length 8cm and width 3cm. Are they congruent?
2. Two triangles have angles 40°, 60°, 80°, but different side lengths. Are they congruent?
3. Triangle PQR has sides 4cm, 4cm, 4cm. Triangle XYZ has sides 4cm, 4cm, 4cm. Are they congruent?
4. Two coins are congruent. What must be true about their sizes?
5. If triangle ABC is congruent to triangle XYZ, and side AB is 6cm, what is the length of side XY?