Question

are these shapes congruent?
g 60 m f
60 in 120° 120°
60 in
h 120° 120° e
60 in
120° 120°
i 60 in j
f 60 in u
60 in 120° 120° 60 in
s 120° 120° p
60 in
120° 120°
r 60 in q
yes
no
submit

Explanation:

Step1: Define congruent polygons

Congruent polygons have all corresponding sides equal in length, and all corresponding angles equal in measure, and can be mapped onto each other via rigid transformations (translation, rotation, reflection).

Step2: Compare side lengths

Both shapes are hexagons with every side measuring 60 in. All corresponding sides are equal:
$GH=TS=60$, $GF=TU=60$, $FE=UP=60$, $EJ=PQ=60$, $JI=QR=60$, $IH=RS=60$

Step3: Compare angle measures

All interior angles of both hexagons are $120^\circ$. All corresponding angles are equal.

Step4: Verify congruence

Since all corresponding sides and angles are equal, the shapes satisfy the definition of congruent polygons.

Answer:

yes