Question

If $∆\mathrm{ABC}~∆\mathrm{EDF}$ and $∆\mathrm{ABC}$ is not similar to $∆\mathrm{DEF}$, then which of the following is not true?

• A. $BC\cdot EF=AC\cdot FD$
• B. $AB\cdot EF=AC\cdot DE$
• C. $BC\cdot DE=AB\cdot EF$
• D. $BC\cdot DE=AB\cdot FD$

Answer 1

The correct option is C

$\mathrm{BC}·\mathrm{DE}=\mathrm{AB}·\mathrm{EF}$

Step 1: Use the properties of similar triangles.

As the provided triangles $ABC$ and $EDF$ are similar so,

$\frac{\mathrm{AB}}{\mathrm{ED}}=\frac{\mathrm{AC}}{\mathrm{EF}}=\frac{\mathrm{BC}}{\mathrm{DF}}$

Take the first two fractions and then write them as an equation, after doing the cross multiplication check the result.

$\begin{array}{rcl}\frac{\mathrm{AB}}{\mathrm{ED}}& =& \frac{\mathrm{AC}}{\mathrm{EF}}\\ & \Rightarrow & \mathrm{AB}·\mathrm{EF}=\mathrm{ED}·\mathrm{AC}\end{array}$

The obtained result is same as the option B so option B is correct.

Take the further two fractions and then write them as an equation, after doing the cross multiplication check the result.

$\begin{array}{rcl}\frac{\mathrm{AC}}{\mathrm{EF}}& =& \frac{\mathrm{BC}}{\mathrm{DF}}\\ & \Rightarrow & \mathrm{AC}·\mathrm{DF}=\mathrm{EF}·\mathrm{BC}\end{array}$

The obtained result is the same as option A so option A is correct.

Take the fractions $\frac{\mathrm{AB}}{\mathrm{ED}}$ and $\frac{\mathrm{BC}}{\mathrm{DF}}$ and then write them as an equation, after doing the cross multiplication check the result.

$\begin{array}{rcl}\frac{\mathrm{AB}}{\mathrm{ED}}& =& \frac{\mathrm{BC}}{\mathrm{DF}}\\ & \Rightarrow & \mathrm{AB}·\mathrm{DF}=\mathrm{BC}·\mathrm{ED}\end{array}$

The obtained result is the same as option D so option D is correct.

The equation provided in option C was not present in any equation so the correct option is option C.