Ignacio wants to prove that ΔABC≅ΔDCB . He says that he knows AC¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ because diagonals in rectangles are congruent. What rule can he use to prove that BC¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ ?

Question

Ignacio wants to prove that  ΔABC≅ΔDCB . He says that he knows  AC¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯  because diagonals in rectangles are congruent. What rule can he use to prove that  BC¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ ?

(1 point)
Responses which answer is correct and why

the Distributive Property
the Distributive Property

the HL Theorem
 the HL Theorem

the Reflexive Property
the Reflexive Property

the Pythagorean Theorem

GPT-4o mini · Answer

The correct answer is **the Reflexive Property**. **Explanation**: The Reflexive Property states that any geometric figure is congruent to itself. In the case of triangles ΔABC and ΔDCB, the side BC is a common side to both triangles. Therefore, we can say that $ BC \cong BC $ due to the Reflexive Property. This congruence helps in establishing the criteria needed to prove that the two triangles are congruent, along with the information Ignacio provided about the congruence of the diagonals.