SIMILARITY AND CONGRUENCY

BASIC COMPETENCE : 1.2. TO IDENTIFY THE PROPERTIES OF TWO SIMILAR AND CONGRUENT TRIANGELS

INDICATOR : TO DETERMINE REQUIREMENTS FOR TWO SIMILAR TRIANGLES TO DETERMINE THE RATIO OF THE SIDES OF TWO TRIANGLES AND FINDING THE SIDE LENGTHS TO DETERMINE REQUIREMENTS FOR TWO CONGRUENT TRIANGLES

LOOK AT THE FIGURE BELOW AB is the height of building BC is the length of image of building B C K KL is the length of flag pole LM is the length of image of flag pole L M

SO THE CORRESPONDING ANGELS ARE THE SAME SIZE  THE CORRESPONDING ANGELS OF BOTH TRIANGLES ARE :  B =  L = 900 C =  M = AND  A =  K SO THE CORRESPONDING ANGELS ARE THE SAME SIZE  50 m 30 m  B C K THE CORRESPONDING SIDES OF BOTH TRIANGLES ARE : = =  5 m 3 m  = = M L

FROM THE EXPLAINATION ABOVE WE CAN SAY THAT : THE CORRESPONDING ANGLES ARE THE SAME SIZE. THE RATIO OF CORRESPONDING SIDES ARE EQUAL. SO, WE CAN SAY THAT TWO TRIANGLES ABOVE ARE SIMILARY.

SO, THE PROPERTIES FOR THE SIMILARITY OF TWO TRIANGLES ARE AS FOLLOWS : 1. THE CORRESPONDING ANGLES ARE THE SAME SIZE. 2. THE RATIO OF CORRESPONDING SIDES ARE EQUAL

LOOK AT THE FIGURE BELOW C K L M P R Q

IF  ABC MOVES TO THE RIGHT SO EXACTLY COVERS TO  KLM, SO WE CAN SAY THAT  ABC AND  KLM ARE CONGRUENT. IF TWO TRIANGLES ARE CONGRUENT IT MUST BE SIMILAR. IF TWO TRIANGLES ARE SIMILAR IT MUST NOT BE CONGRUENT.

LOOK AT THE FIGURE BELOW : C L K A B M AB = KL BC = LM AC = KM ABC AND  KLM ARE CONGRUENT BASED ON ( SIDE , SIDE , SIDE )

C L K A B M AB = KL  B =  L BC = LM SO,  ABC AND  KLM ARE CONGRUENT BASED ON ( SIDE , ANGLE , SIDE )

 ABC AND  KLM ARE CONGRUENT BASED ON ( ANGLE , SIDE , ANGLE )   M B =  L BC = LM  C =  M  ABC AND  KLM ARE CONGRUENT BASED ON ( ANGLE , SIDE , ANGLE )

CONCLUSION : TWO TRIANGLES ARE CALLED SIMILAR IF : THE CORRESPONDING ANGLES ARE THE SAME SIZE. THE RATIO OF THE CORRESPONDING SIDES ARE EQUAL. TWO TRIANGLES ARE CALLED CONGRUENT IF : 1. THE CORRESPONDING SIDES ARE THE SAME SIZE.( SIDE , SIDE , SIDE ) 2. IF THE SIZE OF ONE ANGLE OF TWO TRIANGLES ARE THE SAME AND IT LIES BETWEEN TWO RESPECTIVE SIDES OF THE SAME LENGTH (SIDE , ANGLE , SIDE )

1. THE CORRESPONDING SIDES ARE THE SAME SIZE.( SIDE , SIDE , SIDE ) TWO TRIANGLES ARE CALLED CONGRUENT IF : 1. THE CORRESPONDING SIDES ARE THE SAME SIZE.( SIDE , SIDE , SIDE ) 2. IF THE SIZE OF ONE ANGLE OF TWO TRIANGLES ARE THE SAME AND IT LIES BETWEEN TWO RESPECTIVE SIDES OF THE SAME LENGTH (SIDE , ANGLE , SIDE ) 3. IF THE LENGTH OF ONE SIDE OF TWO TRIANGLES ARE THE SAME AND IT LIES BETWEEN TWO RESPECTIVE ANGLES WITH THE SAME SIZE ( ANGLE , SIDE , ANGLE )