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
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
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'.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CHSL
