5 Views

Question : In $\triangle ABC$ and $\triangle PQR, \angle B=\angle Q, \angle C=\angle R$ and $AB=2PQ$, then the two triangles are:

Option 1: congruent as well as similar

Option 2: neither similar nor congruent

Option 3: similar but not congruent

Option 4: congruent but not similar


Team Careers360 10th Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

Correct Answer: similar but not congruent


Solution :
Given: In the triangles ABC and PQR, $\angle B = \angle Q$, $\angle C = \angle R$
Also, AB = 2PQ
We have to find if the triangles are similar and congruent or not.
Angle-Angle-Angle(AAA) criterion states that if two angles of a triangle are respectively equal to two angles of another triangle, then by the angle sum property of a triangle their third angle will also be equal.
By AAA criterion,
As $\angle B = \angle Q$ and $\angle C = \angle R$, the third angle will also be equal.
$\therefore \angle A = \angle P$
Therefore, the triangles ABC and PQR are similar.
It is given that AB = 2PQ
It is clear that the sides AB and PQ are not equal,
So, the triangles are not congruent.
Therefore, the triangles ABC and PQR are similar but not congruent.
Hence, the correct answer is 'similar but not congruent'.

How to crack SSC CHSL

Candidates can download this e-book to give a boost to thier preparation.

Download Now

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books