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T H E O R E M P Y T H A G O R A S. 5cm. 3cm. 4cm. Yr ochr hirraf yw’r. Pob tro cyferbyn a’r. Felly =. ( ) = ( ) + ( ). =. Yr Hypotenws (yr ochr hirraf). Y ddwy ochr arall. Theorem Pythagoras =. h. a. b. THEOREM PYTHAGORAS. Ymarfer

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slide1

T H E O R E M

P Y T H A G O R A S

slide2

5cm

3cm

4cm

Yr ochr hirraf

yw’r

Pob tro cyferbyn a’r

felly
Felly =

( ) = ( ) + ( )

=

Yr Hypotenws

(yr ochr hirraf)

Y ddwy ochr arall

Theorem Pythagoras

=

h

a

b

slide4

THEOREM PYTHAGORAS

Ymarfer

Ar gyfer y trionglau canlynol, ysgrifennwch Theorem Pythagoras ar eu cyfer

z

g

c

e

b

x

y

d

f

g2 = f2 + e2

c2 = b2 + d2

y2 = x2 + z2

slide5

Camau hawdd i ddarganfod ?

?

8cm

CAM 1 rhifau (mwyaf yn gyntaf)

6cm

CAM 2 sgwario

CAM 3 + neu -

Ochr hirraf?

CAM 3 Ailisraddio √

slide6

Camau hawdd i ddarganfod ?

?

17cm

CAM 1 rhifau (mwyaf yn gyntaf)

13cm

CAM 2 sgwario

CAM 3 + neu -

Ochr hirraf?

CAM 3 Ailisraddio √

slide7

?

Camau hawdd i ddarganfod ?

8cm

5cm

CAM 1 rhifau (mwyaf yn gyntaf)

CAM 2 sgwario

CAM 3 + neu -

Ochr hirraf?

CAM 3 Ailisraddio √

slide8

cm2

cm2

cm2

Yr ochr hirraf

yw’r

Pob tro cyferbyn a’r

slide9

Cyfanswm arwynebedd y ddau sgwar lleiaf yw arwynebedd y sgwar mwyaf.

MAE HYN YN WIR BOB TRO!

THEOREM PYTHAGORAS

YR ATEB

slide10

THEOREM PYTHAGORAS

Mae rheol i'w chael sy'n cysylltu hyd tair ochr triongl ongl sgwâr. Enw'r rheol honno yw Theorem Pythagoras

Defnyddir Theorem Pythagoras i ddarganfod hyd ochr coll mewn triongl ongl sgwâr.

Yr ochr sydd gyferbyn â’r ongl sgwâr yw yr ochr hiraf yn y triongl. Enw’r ochr yma ydy Hypotenws

Hypotenws

slide11

h

a

h2 = a2 + b2

b

THEOREM PYTHAGORAS

Mae Theorem Pythagoras yn dweud:

slide12

x

3cm

4cm

x =25

THEOREM PYTHAGORAS

DARGANFOD HYD YR HYPOTENWS

x2 = 42 + 32

x2 = 16 + 9

x2 = 25

x = 5cm

Cofiwch mai yr hypotenws yw’r ochr hiraf bob tro, felly mae’r ateb yma yn gwneud synnwyr

slide13

THEOREM PYTHAGORAS

Ymarfer

Darganfyddwch hyd yr hypotenws ar gyfer y trionglau canlynol

6m

x

8mm

11m

x

6mm

x

7cm

24cm

slide14

THEOREM PYTHAGORAS

DARGANFOD HYD YR OCHR ARALL

52 = 42 + x2

5cm

25 = 16 + x2

x

25 – 16 = x2

9 = x2

4cm

√9 = x

x = 3cm

slide15

THEOREM PYTHAGORAS

Ymarfer

Darganfyddwch yr hyd coll ar gyfer y trionglau canlynol

5.2m

x

26cm

x

18.7m

10cm

14.7mm

6.2mm

x

slide16

6cm

8cm

THEOREM PYTHAGORAS

DARGANFOD HYD OCHRAU TRIONGL ISOSGELES

Cofiwch: Mae Theorem Pythagoras dim ond yn gweithio ar gyfer trionglau ongl sgwâr, felly mae’n rhaid rhannu’r triongl yn ddau er mwyn cael triongl ongl sgwâr.

x

x

6cm

x2 = 62 + 42

x2 = 36 + 16

x2 = 52

4cm

x = √52

x = 7.2cm (1.ll.d)