Question

$\text{In the given figure ar}\left(△BUG\right)\text{is equal to}\text{ar}\left(△CUP\right),\text{then which of the following}\text{statements are true?}$

• A. $\text{BU is not equal CU}$
• B. $\text{BU is equal to CU}$
• C. $\text{BC is parallel to PG.}$
• D. $\text{BC is not parallel to PG.}$

Answer 1

Answer: (B), (C)

The correct options are
B $\text{BU is equal to CU}$
C $\text{BC is parallel to PG.}$

Two triangles on the same base (or equal bases) and between the same parallels have equal areas.

$\therefore$ $\text{If ar}\left(△BUG\right)=\text{ar}\left(△CUP\right),$
$\left(△BUG\right)\text{and}\left(△CUP\right)\text{have the same}\text{base and are between the same}\text{parallels.}$

$\Rightarrow \text{BU is equal to CU and BC is}$$\text{parallel to PG.}$