Question

If in triangle abc and triangle qpr, ab/pq=bc/pr, then prove that they will be similar when angleb=anglep

Answer 1

Given:- There are two triangles ΔABC and ΔQPR such that $\frac{AB}{QP}=\frac{BC}{PR}$

To Prove:- ΔABC is similar to ΔQPR iff ∠B=∠P

THEOREM USED:- SAS SIMILARITY RULE-The SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are equal, then the two triangles are similar.

Proof:- Let us suppose that ∠ABC is equal to ∠QPR.

Now , In ΔABC and ΔQPR,

$\frac{AB}{QP} =\frac{BC}{PR}$ [given]

∠ABC=∠QPR

In above case ratio of two sides is equal and angles included in between the sides is also equal.

Hence By SAS Similarity Rule,

ΔABC is similar to  ΔQPR

Hence proved.