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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
In $\triangle\text{ABC}$ and $\text{ DEF},\angle\text{B}= \angle\text{E},\angle\text{F}=\angle\text{C}$ and $\text{AB} =3\text{DE}$ Then, the two traingles are :
  • A
    Congruent but not similar
  • ✓
    Similar but not congruent
  • C
    Neither congruent nor similar
  • D
    Congruent as well as similar
✓

Answer

Correct option: B.
Similar but not congruent
in $\triangle\text{ABC}$ and $\triangle\text{DEF}$,
$\angle\text{B}= \angle\text{E},\angle\text{F}=\angle\text{C}$ and $\text{AB}=3 \text{DE}$
By $\text{AA}$ similarity criterion,
$\triangle\text{ABC}\sim\triangle\text{DEF}$
$\text{AB}=3\text{DE}$
$=\frac{\text{AB}}{\text{DE}}=3$
$=\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{AC}}{\text{DF}}=3$
For triangles to be congruent, the ratio of sides must be $1$
Therefore, triangles are similar but not congruent.

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