State which pairs of triangles in Fig. 6.34 are similar....

Key Concepts

Triangle Similarity

Triangle similarity is a fundamental geometric concept where two triangles are considered similar if their corresponding angles are congruent and their corresponding sides are in proportion. This concept allows for the use of indirect measurements and scaling in various geometric problems.

Similarity Criteria

The similarity criteria, such as Angle-Angle (AA), Side-Angle-Side (SAS), or Side-Side-Side (SSS), provide systematic methods to determine whether two triangles are similar. Identifying corresponding angles and proportional sides forms the basis of proving similarity between triangles.

Symbolic Representation of Similar Triangles

Similar triangles are often denoted symbolically using the similarity symbol (?), for example, triangle ABC ? triangle DEF. This notation signifies that the triangles have equivalent corresponding angles and proportional sides, making it a concise and universal language in geometric proofs.

Transcript

00:01 We are going to do problem number one.

00:02 In this question we have to just state which pair of triangles are similar.

00:07 And we have to write the similarity criteria used that we will use to answer the question and also write pair of similar triangles in the symbolic form.

00:20 There of similar triangle in symbolic form.

00:22 So if we just go through first part, if we go through first part, then if we can see that all corresponding angles are same like angle.

00:31 Angle a is equals to angle p angle b is equals to angle q angle c is equal to angle r means by a a angle angle angle similarity criteria similarity criteria let me write here similarity criteria triangle a b c is similar to triangle pqr okay so first pair is similar we are going to just proceed to the second part in second part that i just write it here in second part again the sites are given so we will write here in second part it is given that a b is given as two so a b is given as two and pq is given as 6 okay now bc is given as 2 .5 and this one qr is given as 4 now pq or ac let me write here ac ac this is given as 3 and pr this is given as 5 now if you see the ratio that ab divided by qr this is equals to bc divided by rp that is equals to c a divided by pq okay so this shows us that by using s s s similarity criterion okay by s s similarity criteria the given triangle is congruent so the triangle which is congruent here is triangle a b c is congruent to triangle qrp okay so this is the answer of second part now let us just move to the third part here now we'll just observe the given case so in this case if we see the sites are given as lm is given as 2 .7 m p is given as 2 l p is given as 3 similarly on the other triangle d .e is given as 4 and let me just it is this part yeah ef is given as 5 df is given as 6 now we have to just see whether the ratio are same or not okay so if you see mp mp divided by de this is equals to this is equals to 2 by 4 which is equals to 1 by 2 and similarly if you just check it for pl pl pl divided by df then this will be equal to 3 by which is equals to 1 by 2 so you have to check for the last pair that is for lm divided by e f so lm in this case is it will start it here that is 2 .7 and here this is 5 so this is 27 divided by 50 and if you just try to we just can't make it in more simpler form so the ratios are not similar so we can say the given triangle triangle l mp is not similar to triangle to triangle d ef okay not similar now we will just move to the fourth part we are done with the third part in fourth part this given triangle m and l and also given triangle pqr okay so angle m is equals to angle q and mn by pq and m .m.

05:34 By p.

05:35 And m l by q are they both are given in a ratio so by side angle side criteria side similarity criteria given triangle is similar is similar so let us just write here triangle m and l is similar to triangle qpr...

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