Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Show that the relation R defined in the set A of all triangles as R = {(T 1 , T 2 ) : T 1 is similar to T 2 }, is equivalence relation. Consider three right angle triangles T 1 with sides 3, 4, 5, T 2 with sides 5, 12, 13 and T 3 with sides 6, 8, 10.

Q.11 Show that the relation R defined in the set A of all triangles as R = \{(T_1 , T_2 ) : T_1 \;is\; similar \;to\; T_2 \}, is equivalence relation. Consider three right-angled triangles: T1 with sides 3, 4, and 5, T2 with sides 5, 12, and 13, and T3 with sides 6, 8, and 10. Which triangles among T1, T2, and T3 are related?

 

Answers (1)

best_answer

R = \{(T_1 , T_2 ) : T_1 \;is\; similar \;to\; T_2 \}

All triangles are similar to itself, so it is reflexive.

Let,

(T_1,T_2) \in R  i.e.T1 is similar to T2

T1 is similar to T2; T2 is similar to T1, i.e. (T_2,T_1) \in R

Hence, it is symmetric.

Let,

(T_1,T_2) \in R  and  (T_2,T_3) \in R  i.e. T1 is similar to T2  and T2 is similar toT3 .

\RightarrowT1 is similar toT3   i.e. (T_1,T_3) \in R

 Hence, it is transitive,

Thus,  R = \{(T_1 , T_2 ) : T_1 \;is\; similar \;to\; T_2 \}, is equivalence relation.

Now , we see ratio of sides of triangle T1 and T3 as shown

 \frac{3}{6}=\frac{4}{8}=\frac{5}{10}=\frac{1}{2}

i.e. ratios of sides of T1 and T3 are equal.Hence, T1 and T3 are related.

 

 

 

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

No changes in exam, IA system: CBSE rebuts claims of syllabus reduction, open book exams in 2025
anam-khan

Fact-check: CBSE hasn't reduced syllabus by 15%, internal assessments will not be 40% of score in 2025
anam-khan

CBSE date sheet 2025 for Classes 10, 12 likely in November last week: Reports

Latest Question