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Congruent and Similar Triangles A PERESENTATION BY RITIK XF T Saraswati Bal Mandir Sr. Sec. Schoo Nehru Nagar ND=65

Congruent and similar triangle by ritik

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Page 1: Congruent and similar triangle by ritik

Congruent and Similar Triangles

A PERESENTATION BYRITIK

XF

GLT Saraswati Bal Mandir Sr. Sec. SchoolNehru Nagar ND=65

Page 2: Congruent and similar triangle by ritik

IntroductionRecognizing and using congruent and similar shapes can make calculations and design work easier. For instance, in the design at the corner, only two different shapes were actually drawn. The design was put together by copying and manipulating these shapes to produce versions of them of different sizes and in different positions.

Page 3: Congruent and similar triangle by ritik

Similar and Congruent Figures

• Congruent triangles have all sides congruent and all angles congruent.

• Similar triangles have the same shape; they may or may not have the same size.

Page 4: Congruent and similar triangle by ritik

Note: Two figures can be similar but not congruent, but they can’t be congruent but not similar. Think about why!

Similar and Congruent Figures

Page 5: Congruent and similar triangle by ritik

ExamplesThese figures are similar and congruent. They’re the same shape and size.

These figures are similar but not congruent. They’re the same shape, but not the same size.

Page 6: Congruent and similar triangle by ritik

Ratios and Similar Figures• Similar figures have corresponding

sides and corresponding angles that are located at the same place on the figures.

• Corresponding sides have to have the same ratios between the two figures.

• A ratio is a comparison between 2 numbers (usually shown as a fraction)

Page 7: Congruent and similar triangle by ritik

Ratios and Similar Figures

Example

A E

C

F

D

G H

B

These sides correspond:

AB and EFBD and FHCD and GHAC and EG

These angles correspond:

A and EB and FD and HC and G

Page 8: Congruent and similar triangle by ritik

Ratios and Similar Figures

Example

7 m

3 m 6 m

14 m

These rectangles are similar, because the ratios of these corresponding sides are equal:

7 143 6

3 67 14

7 314 6

14 67 3

Page 9: Congruent and similar triangle by ritik

• A proportion is an equation that states that two ratios are equal.

• Examples:4 8

10n

63 2

m

n = 5 m = 4

Proportions and Similar Figures

Page 10: Congruent and similar triangle by ritik

Proportions and Similar FiguresYou can use proportions of corresponding sides to figure out unknown lengths of sides of polygons. 16

m

10 m

n

5 m

10/16 = 5/n so n = 8 m

–Solve for n:

Page 11: Congruent and similar triangle by ritik

Similar triangles• Similar triangles are triangles with

the same shapeFor two similar triangles, • corresponding angles have the same measure• length of corresponding sides have the same

ratio

65o

25o

A4 cm 2cm

12cmB

Example

Angle 1 = 90o Side B = 6 cm

Page 12: Congruent and similar triangle by ritik

Similar Triangles

Ways to Prove Triangles Are Similar

Page 13: Congruent and similar triangle by ritik

Similar triangles have corresponding angles that are CONGRUENT and

their corresponding sides are PROPORTIONAL.

610

8

3

4

5

Page 14: Congruent and similar triangle by ritik

But you don’t need ALL that information to be able to tell that two

triangles are similar….

Page 15: Congruent and similar triangle by ritik

AA Similarity• If two (or 3) angles of a triangle are congruent to

the two corresponding angles of another triangle, then the triangles are similar.

25 degrees 25 degrees

Page 16: Congruent and similar triangle by ritik

SSS Similarity• If all three sides of a triangle are

proportional to the corresponding sides of another triangle, then the two triangles are similar.

18

12

8

12

1421

23

1421

23

1218

23

812

Page 17: Congruent and similar triangle by ritik

THE END