Question

Complete each statement from the information given and the triangle criterion you used. If the triangles cannot be shown to be congruent, leave the box for the second triangle blank and choose for reason “Cannot be determined.”

CARBON - regular hexagon.
∆CAN ≅ ∆ _____ by _____

Answer 1

The answer is triangle CAN is congruent to triangle BOR by SSS.

Answer 2

Answer: ∆CAN ≅Δ BRO by SSS congruence rule.

Explanation:

It is given that CARBON is a regular polygon.

Since all sides of a regular polygon are equal.

Therefore, CA=AR=RB=BO=ON=NC .....................(1)

In ΔANO and ΔORA

∠ANO=∠ORA [each 90°]

OA=OA [same]

NO=AR [from (1)]

∴ ΔANO ≅ ΔORA by RHS congruence rule

⇒NA=OR [by CPCT]

Now in ∆CAN and Δ BRO..............(2)

CN=OB=CA=RB.............[from (1)]

NA= OR [from (2)]

∴∆CAN ≅Δ BRO by SSS congruence rule.