Cambridge International Mathematics

Lines, angles and polygons (Chapter 4) 101

PROPERTIES

The following properties are associated with the isosceles triangle theorem:

Property 1: If a triangle has two equal angles then it is isosceles.

Property 2: The angle bisector of the apex of an isosceles triangle bisects

the base at right angles.

Property 3: The perpendicular bisector of the base of an isosceles triangle

passes through its apex.

²

² Can you proveProperty 2using triangle

congruence?

Example 4 Self Tutor

Findx, giving brief reasons:

ab

a As AB=AC, the triangle is isosceles

) ABCb =xo also

Now x+x+ 38 = 180 fangles of a¢g

) 2 x= 180¡ 38

) 2 x= 142

) x=71

b As PR=QR, the triangle is isosceles

) QbPR=52o fisosceles¢theoremg

) x=52+52 fexterior angle theoremg

) x= 104

GEOMETRY

PACKAGE

VIDEO

CLIP

aa

Figure 1

aa

Figure 2

A

B

C

x°

38°

Q

P

R

52° x°

A

B

C

x°

x°

38°

Q

P

R

52° x°

52°

To prove , Sam tries to use

Figure and triangle congruence.

Will he be successful?

Why or why not? Could Sam be

successful using Figure?

Property 1

1

2

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Y:\HAESE\IGCSE01\IG01_04\101IGCSE01_04.cdr Friday, 12 September 2008 3:33:51 PM PETER