Question

maya is designing a puzzle game where players must identify congruent shapes to unlock levels. in level 7, she creates hexagonal tiles with specific patterns. maya notices that some tiles can be rotated and flipped to match others exactly, while some look similar but are actually different sizes. to make the game challenging but fair, she needs to ensure that only truly congruent tiles will unlock the next level.
question 1
maya has created four hexagonal tiles for her puzzle. tile a has side lengths of 2 cm each and interior angles of 120°. which of the following tiles would be congruent to tile a?
tile e: side lengths of 1.5 cm each, interior angles of 120°
tile d: side lengths of 2 cm each, interior angles of 110°
tile b: side lengths of 2 cm each, interior angles of 120°, but rotated 60°
tile c: side lengths of 4 cm each, interior angles of 120°

Explanation:

Step1: Recall the definition of congruent shapes

Congruent shapes have the same size and shape. That means all corresponding side lengths and angle measures are equal.

Step2: Analyze Tile E

Tile E has side lengths \(1.5\) cm while Tile A has side lengths \(2\) cm. Since side lengths are not equal, Tile E is not congruent to Tile A.

Step3: Analyze Tile D

Tile D has interior angles of \(110^{\circ}\) while Tile A has interior angles of \(120^{\circ}\). Since angle measures are not equal, Tile D is not congruent to Tile A.

Step4: Analyze Tile B

Tile B has side lengths \(2\) cm (same as Tile A) and interior angles of \(120^{\circ}\) (same as Tile A). Rotation (\(60^{\circ}\) in this case) does not change the size or shape of a polygon. So, Tile B is congruent to Tile A.

Step5: Analyze Tile C

Tile C has side lengths \(4\) cm while Tile A has side lengths \(2\) cm. Since side lengths are not equal, Tile C is not congruent to Tile A.

Answer:

Tile B