Question : In $\Delta ABC$, two points $D$ and $E$ are taken on the lines $AB$ and $BC,$ respectively in such a way that $AC$ is parallel to $DE$. Then $\Delta ABC$ and $\Delta DBE$ are:
Option 1: Similar only if $D$ lies outside the line segment $AB$.
Option 2: Congruent only if $D$ lies outside the line segment $AB$.
Option 3: Always similar.
Option 4: Always congruent.

Question

Question : In $\Delta ABC$, two points $D$ and $E$ are taken on the lines $AB$ and $BC,$ respectively in such a way that $AC$ is parallel to $DE$. Then $\Delta ABC$ and $\Delta DBE$ are:

Option 1: Similar only if $D$ lies outside the line segment $AB$.

Option 2: Congruent only if $D$ lies outside the line segment $AB$.

Option 3: Always similar.

Option 4: Always congruent.

Team Careers360 · Accepted Answer

Correct Answer: Always similar.

Solution :
We have, $D$ and $E$ are the points on $AB$ and $BC$. Such that $AC$ is parallel to $DE$.
In $\Delta ABC$ and $\Delta DBE$,
$\angle A=\angle D$ (Corresponding angle)
$\angle C=\angle E$ (Corresponding angle)
$ herefore \Delta ABC\sim\Delta DBE$ (by AA similarity)
Hence, the correct answer is Always similar.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Online Courses

Products

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Student Visas

Exams

Top Schools

Products & Resources

NCERT Study Material

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CHSL

Download the Careers360 App on your Android phone

Sign In/Sign Up