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Mathematics

Grade9

Easy

Question

Given the triangles ABC and DEF as shown at the right. In addition to the markings, AF = CD. Identify which method is NOT to be used to prove the triangles congruent.

SAS
SSS
AAS
HL

hint Hint:

$I n space t h i s space q u e s t i o n comma space w e space h a v e space t o space f i n d space w h i c h space m e t h o d space i s space n o t space u s e d space t o space p r o v e space c o n g r u e n c e space i f space i t space i s space g i v e n space t h a t space i n space increment A B C space a n d space increment D E F comma space angle B equals angle angle E space comma space B C equals E F space a n d space A F equals C D. space F i r s t l y space w e space c a n space s a y space t h a t space angle F equals angle C space a s space o p p o s i t e space i n t e r i o r space a n g l e s space o f space p a r a l l e l space l i n e s space a r e space e q u a l space a l s o space a s space A F equals C D rightwards double arrow A F plus F C equals C D plus F C rightwards double arrow A C equals D F. space F u r t h e r space w e space w i l l space p r o v e space c o n g r u e n c e space i n space e v e r y space w a y space p o s s i b l e space a n d space t h e space w h i c h space w o n apostrophe t space b e space u s e d space w i l l space b e space t h e space r e q u i r e d space m e t h o d. space S A S thin space i s space s i d e space a n g l e space s i d e comma space S S S space i s space s i d e space s i d e space s i d e comma space A A S space i s space a n g l e space a n g l e space s i d e space a n d space H L space i s space h y p o t e n u s e space l e g left parenthesis h y p o t e n u s e space a n d space o n e space s i d e right parenthesis.$

The correct answer is: SSS

$A s space E F thin space parallel to thin space B C space a n d space A D space c u t space b o t h space t h e space l i n e s space s o space a n g l e s space f o r m e d space o n space o p p o s i t e space s i d e s space a r e space e q u a l. space S o comma space angle F space equals space angle C. space space N o w comma space A F space space space space space space space space space space space space equals space C D space space space space space space space space a d d i n g space F C space o n space b o t h space s i d e s comma space space space space space space space space rightwards double arrow A F plus F C space equals space C D space plus F C space space space space space space space rightwards double arrow A C space space space space space space space space space space equals space D F A s space angle F space equals angle C comma space space A C equals D F space a n d space B C equals E F S o comma space triangle A B C approximately equal to triangle D E F space left parenthesis b y space S A S space c o n g r u e n c e right parenthesis A s space angle B equals angle E equals 90 degree comma space angle F space equals angle C space a n d space A C equals D F S o comma space triangle A B C approximately equal to triangle D E F space left parenthesis b y space A A S space c o n g r u e n c e right parenthesis A l s o comma space a s space angle B equals angle E equals 90 degree comma space A C equals D F left parenthesis h y p o t e n u s e right parenthesis space a n d space B C equals E F S o comma space triangle A B C approximately equal to triangle D E F space left parenthesis b y space H L space c o n g r u e n c e right parenthesis$
As AC = DF, BC = EF but AB $not equal to$ DE.
So, SSS is not used to prove triangle congruent.

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