congruent triagles

CONGRUENT TRIANGLES:

CONGRUENT TRIANGLES

CONGRUENT FIGURES:

CONGRUENT FIGURES Figures, which have same shape and size are called congruent figures. A plane figure F 1 is said to be congruent to F 2 , if F 1 ,when superposed over F 2 , covers it exactly F 1 F 2 F 1 F 2 F 1 F 2

CONGRUENT FIGURES:

CONGRUENT FIGURES Figures, which have same shape and size are called congruent figures. A plane figure F 1 is said to be congruent to F 2 , if F 1 ,when superposed over F 2 , covers it exactly F 1 F 2 F 1 F 2 F 1 F 2

Congruence of triangles:

Congruence of triangles A B C D E F A(D) B(E) C(F)

CORRESPONDING PARTS (MATCHING PARTS):

CORRESPONDING PARTS (MATCHING PARTS) The two triangles coincide when we make the matching ABC<->DEF. So we say that under the matching ABC<->DEF, ∆ABC is congruent to ∆DEF. The other matching do not give a congruence. ABC<->DEF ABC<->DFE ABC<->EDF ABC<->EFD ABC<->FDE ABC<->FED The two triangles cover each other exactly. It follows immediately that: AB=DE BC=EF AC=DF ∟A= ∟D ∟B=∟E ∟C=∟F

Slide 9:

As ∆ABC is congruent to ∆DEF, t he matching parts (corresponding parts) of congruent triangles are equal.

CONDITIONS FOR CONGRUENCE OF TRIANGLES:

CONDITIONS FOR CONGRUENCE OF TRIANGLES SAS (SIDE-ANGLE-SIDE) ASA (ANGLE-SIDE-ANGLE) SSS (SIDE-SIDE-SIDE) RHS (RIGHT ANGLE-HYPOTENUSE-SIDE)

SAS congruence condition:

SAS congruence condition Two triangles are congruent if two sides and in the included angle of one triangle are respectively equal to the two sides and the included angle of the other. A B C D E F

SAS congruence condition:

SAS congruence condition Two triangles are congruent if two sides and in the included angle of one triangle are respectively equal to the two sides and the included angle of the other. A B C D E F

ASA congruence condition:

ASA congruence condition Two triangles are congruent, if two angles and the included side of one triangle are respectively equal to the two angles and the included side of the other triangle A B C D E F 6 CM. 6 CM. 35 º 50 º 50º 35º

ASA congruence condition:

ASA congruence condition Two triangles are congruent, if two angles and the included side of one triangle are respectively equal to the two angles and the included side of the other triangle A B C 6 CM. 35 º 50 º f d e 50 35

SSS congruence condition:

SSS congruence condition Two triangles are congruent, if the three sides of one triangle are respectively equal to the three corresponding sides of the other triangle. 5 CM. 5 CM. 4 CM. 4 CM. 3 CM. 3 CM. A B C D E F

SSS congruence condition:

SSS congruence condition Two triangles are congruent, if the three sides of one triangle are respectively equal to the three corresponding sides of the other triangle. 5 CM. 5 CM. 4 CM. 4 CM. 3 CM. 3 CM. A B C D E F

RHS congruence condition:

RHS congruence condition The two triangles are congruent, if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and the one side of the other triangle. A B C D E F 5 CM. 13 CM. 5 CM. 13 CM. 90 º 90 º

RHS congruence condition:

RHS congruence condition The two triangles are congruent, if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and the one side of the other triangle. A B C D E F 5 CM. 13 CM. 5 CM. 13 CM. 90 º 90 º