Everything Maths Grade 10

Similarity EMA5V

Two triangles are similar if one triangle is a scaled version of the other. This means that their corresponding
angles are equal in measure and the ratio of their corresponding sides are in proportion. The two triangles have
the same shape, but different scales. Congruent triangles are similar triangles, but not all similar triangles are
congruent. We use jjj to indicate that two triangles are similar.

The following table describes the requirements for similarity:

Rule Description Diagram

AAA

(angle, angle,

angle)

If all three pairs of corresponding

angles of two triangles are equal,

then the triangles are similar.

B C

䄀

a

b c E F

䐀

a

b c

A^=D^,B^=E^,C^=F^

)△ABCjjj △DEF

SSS

(side, side, side)

If all three pairs of correspond-

ing sides of two triangles are in

proportion, then the triangles are

similar.

N L

䴀

S T

刀

MN

RS =

ML

RT =

NL

ST

)△M N Ljjj △RST

The order of letters for similar triangles is very important. Always label similar triangles in corresponding order.
For example,

△M N Ljjj △RSTis correct; but

△M N Ljjj △RT Sis incorrect.

NOTE:

You might seeused to show that two triangles are similar. This is the internationally recognised symbol for

similarity.

VISIT:

The following video explains similar triangles.

See video:2G6Datwww.everythingmaths.co.za

The theorem of Pythagoras EMA5W

If△ABCis right-angled withB^= 90°, thenb^2 =a^2 +c^2.
Converse:Ifb^2 =a^2 +c^2 , then△ABCis right-angled withB^= 90°.

C B

䄀

戀

愀

挀

246 7.2. Triangles