If in two triangles ABC and DEF, ∠A=∠E, ∠B=∠F then which of the following is not true

If in two triangle ABC and DEF, ∠A = ∠E, ∠B = ∠F, then which of the following is not true?

Question:

If in two triangle $\mathrm{ABC}$ and $\mathrm{DEF}, \angle \mathrm{A}=\angle \mathrm{E}, \angle \mathrm{B}=\angle \mathrm{F}$, then which of the following is not true?

(a) BCDF=ACDE
(b) ABDE=BCDF
(c) ABEF=ACDE
(d) BCDF=ABEF

Solution:

 In ΔABC and ΔDEF

$\angle \mathrm{A}=\angle \mathrm{E}$

$\angle \mathrm{B}=\angle \mathrm{F}$

$\therefore \triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are similar triangles.

Hence $\frac{\mathrm{AB}}{\mathrm{EF}}=\frac{\mathrm{BC}}{\mathrm{FD}}=\frac{\mathrm{CA}}{\mathrm{DE}}$

Hence the correct answer is (b).

If in two triangle ABC and DEF, ∠A = ∠E, ∠B = ∠F, then which of the following is not true?

(a)\[\frac{BC}{DF} = \frac{AC}{DE}\]

(b)\[\frac{AB}{DE} = \frac{BC}{DF}\]

(c)\[\frac{AB}{EF} = \frac{AC}{DE}\]

(d)\[\frac{BC}{DF} = \frac{AB}{EF}\]

• \[\frac{BC}{DF} = \frac{AC}{DE}\]

• \[\frac{AB}{DE} = \frac{BC}{DF}\]

• \[\frac{AB}{EF} = \frac{AC}{DE}\]

• \[\frac{BC}{DF} = \frac{AB}{EF}\]

 In ΔABC and ΔDEF

`∠ A = ∠ E`

`∠ B = ∠ F`

∴ ΔABC and ΔDEF are similar triangles.

Hence `(AB)/(EF)=(BC)/(FD)=(CA)/(DE)`

Hence the correct answer is (b).

Concept: Triangles Examples and Solutions

  Is there an error in this question or solution?