Question

Given that ABC - ZDBE, which statement must be true?

a) ZABC - ZABD
b) ZABD = ZCBE
c) ZCBD = ZDBE
d) CBD = ZABC

Answer 1

Statement c) ZCBD = ZDBE must be true.

Step-by-step explanation:

To understand which statement must be true given ABC - ZDBE, we need to analyze the given expression and the options:

1. a) ZABC - ZABD: This option takes the segments ZABC and ZABD as subtracted quantities. It does not align with the given expression ABC - ZDBE.
2. b) ZABD = ZCBE: This option equates the segments ZABD and ZCBE, which are not present in the given expression ABC - ZDBE.
3. c) ZCBD = ZDBE: This option equates the segments ZCBD and ZDBE, which align with the given expression ABC - ZDBE. Therefore, this statement must be true.
4. d) CBD = ZABC: This option equates the segments CBD and ZABC, which are not present in the given expression ABC - ZDBE.

From the analysis, we can conclude that statement c) ZCBD = ZDBE must be true.