1 / 14

SIMILAR

SIMILAR. TRIANGLES. Presentation by Shweta Singh Huria, TGT(Maths), KV,Sector-8, Rohini, New Delhi. In geometry , two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other

graham
Télécharger la présentation

SIMILAR

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SIMILAR TRIANGLES Presentation by Shweta Singh Huria, TGT(Maths), KV,Sector-8, Rohini, New Delhi.

  2. In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely. Turning the paper over is permitted. Congruence of two triangles In elementary geometry the word congruent is often used as follows.The word equal is often used in place of congruent for these objects. Two line segments are congruent if they have the same length. Two angles are congruent if they have the same measure. Two circles are congruent if they have the same diameter. In this sense, two plane figures are congruent implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters and area

  3. m your earlier classes. In Class IX, you have studied congruence of triangles in detail. Recall that two figures are said to be congruent, if they have the same shape and the same size. In this chapter, we shall study about those figures which have the same shape but not necessarily the same size. Two figures having the same shape (and not necessarily the same size) are called similar figures. We shall study about those figures which have the same shape but not necessarily the same size

  4. Consider any two (or more) circles . Are they congruent? Since all of them do not have the same radius, they are not congruent to each other. Note that some are congruent and some are not,but all of them have the same shape.So they all are, what we call, similar.Two similar figures have the sameshape but not necessarily the same size. Therefore, all circles are similar.What about two (or more) squares or two (or more) equilateral triangles /As observed in the case of circles, here also all squares are similar and all equilateral triangles are similar. From the above, we can say that all congruent figures are similar but the similar figures need not be congruent.

  5. we can say that all congruent figures are similar but the similar figures need not be congruent.

  6. For example, all circles are similar to each other,all squaresare similar to each other, and all equilateral triangles are similar to each other.

  7. A D E B F C = = BC AB AC EF DF DE Similar triangles are triangles that have the same shape but not necessarily the same size. ABCDEF When we say that triangles are similar there are several repercussions that come from it. AD BE CF

  8. If we need to prove that a pair of triangles are similar how many of those statements do we need? Because we are working with triangles and the measure of the angles and sides are dependent on each other. We do not need all six. There are three special combinations that we can use to prove similarity of triangles. 1. SSS Similarity Theorem  3 pairs of proportional sides 2. SAS Similarity Theorem  2 pairs of proportional sides and congruent angles between them 3. AA Similarity Theorem  2 pairs of congruent angles

  9. E A 13 9.6 10.4 5 B C 12 D F 4 1. SSS Similarity Theorem  3 pairs of proportional sides ABC  DFE

  10. L G 7.5 5 70 H 70 I 7 J K 10.5 2. SAS Similarity Theorem  2 pairs of proportional sides and congruent angles between them mH = mK GHI  LKJ

  11. L G 7.5 5 50 H 50 I 7 J K 10.5 The SAS Similarity Theorem does not work unless the congruent angles fall between the proportional sides. For example, if we have the situation that is shown in the diagram below, we cannot state that the triangles are similar. We do not have the information that we need. Angles I and J do not fall in between sides GH and HI and sides LK and KJ respectively.

  12. Q M 70 50 N 50 70 O P R 3. AA Similarity Theorem  2 pairs of congruent angles mN = mR MNO  QRP mO = mP

  13. T X Y 34 34 34 34 59 59 87 59 Z S U It is possible for two triangles to be similar when they have 2 pairs of angles given. mT = mX mS = mZ mS = 180- (34 + 87) TSU  XZY mS = 180- 121 mS = 59

More Related