Take a good look at this chess set—not the chess pieces, but the spaces where they sit. What do you notice about the design of the board?
Question
Is there a geometry term that describes the spaces where a player can move a chess piece?
The spaces are congruent—they are exactly the same shape and size. The spaces are different colors, but this difference does not keep them from being congruent.
Any two shapes are said to be congruent when they are exactly the same shape and size. In other words, all corresponding sides are congruent and all corresponding angles are congruent.
Question
How can you tell—for sure—that these two rectangles are congruent?
The corresponding sides of the rectangle are congruent, and we know this because the sides are marked with hash marks that match. Since these are rectangles, we know that all corresponding angles are congruent—they are right angles.
\(\mathsf{ \overline{DC} }\) ≅ \(\mathsf{ \overline{SR} }\)
\(\mathsf{ \overline{AB} }\) ≅ \(\mathsf{ \overline{PQ} }\)
\(\mathsf{ \overline{DA} }\) ≅ \(\mathsf{ \overline{SP} }\)
\(\mathsf{ \overline{CB} }\) ≅ \(\mathsf{ \overline{RQ} }\)
The same principles of congruence hold true for triangles. Analyze the following congruent triangles.
Question
Can you name the pairs of congruent sides and pairs of congruent angles in the triangles above?
| \(\small\mathsf{ \overline{AB} ≅ \overline{DE}, }\) | \(\small\mathsf{ \overline{AC} ≅ \overline{DF}, }\) | \(\small\mathsf{ \overline{BC} ≅ \overline{EF},}\) |
| \(\small\mathsf{ \angle A ≅ \angle D, }\) | \(\small\mathsf{ \angle B ≅ \angle E, }\) | \(\small\mathsf{ \angle C ≅ \angle F }\) |
