CONGRUENT TRIANGLES : CONGRUENT TRIANGLES BY- KUSHASHWA RAVI SHRIMALI
CLASS – VII
ROLL NO. - 707
CONGRUENT FIGURES : CONGRUENT FIGURES TWO OR MORE FIGURES ARE SAID
TO BE CONGRUENT TO EACH OTHER IF THEY OVERLAP EACH OTHER.
CONGRUENT THINGS : CONGRUENT THINGS
CAN TRIANGLES ALSO BE CONGRUENT? : CAN TRIANGLES ALSO BE CONGRUENT? SEEMS LIKE A JOKE ???????????
YES !!! : YES !!! YES!!! Triangles can also be congruent
but there are some necessities.
What are those ?
POINTS THAT MAKE TRIANGLES CONGRUENT : POINTS THAT MAKE TRIANGLES CONGRUENT FOR A TRIANGLE TO BE CONGRUENT IT MUST SATISFY AT LEAST ONE OF THE FOLLOWING CONGRUENCY CRITERION-
SSS congruency criterion – SIDE – SIDE – SIDE
SAS congruency criterion – SIDE – ANGLE – SIDE
ASA congruency criterion – ANGLE – SIDE – ANGLE
RHS congruency criterion – RIGHT ANGLE – HYPOTENUSE - SIDE
SSS congruency criterion – SIDE – SIDE – SIDE : SSS congruency criterion – SIDE – SIDE – SIDE
WHAT IS SSS CONGRUENCE CRITERION IN TRIANGLES? : WHAT IS SSS CONGRUENCE CRITERION IN TRIANGLES? In the SSS congruence criterion the corresponding sides of the triangles are equal.
Hence the name of this rule: Side-Side-Side, SSS
PROBLEMS : PROBLEMS Question A.1: ABC and ABD are two triangles such that AD=BC, BD=AC. Prove that triangles ABC and ABD are congruent.
SOLUTION OF QUESTION A.1 : SOLUTION OF QUESTION A.1 In triangles ABC and ABD, AD=BC and BD=AC.To prove: Triangle ABC and ABD are congruent to each other.Solution:Comparing triangles ABC and ABD ,BC = AD (given)AC = BD (given)AB = AB (common side to both triangles)
Using the SSS postulate it proves that triangles ABC and ABD are congruent .
ASA CONGRUENCE CRITERION : ASA CONGRUENCE CRITERION
ASA CONGRUENCE CRITERION : ASA CONGRUENCE CRITERION If two angles and the included side of one triangle (Angle-Side-Angle, ASA) are equal to two angles and included side of another triangle, then the triangles are congruent. An included side is the side between the two given angles.
PROBLEMS : PROBLEMS Q.B.1: Suppose we have two triangles, ΔPQR and ΔXYZ, such that PR = XZ.
If we have to show ΔPQR ≅ ΔZYX by using ASA congruency criterion, then which two equalities are required?
SOLUTION OF Q.B.1 : SOLUTION OF Q.B.1 We are given that PR = XZ
In order to show ΔPQR ≅ ΔZYX by ASA congruency criterion, the two angles of ΔPQR, which include the side PR, should be equal to the two angles of ΔXYZ, which include the side XZ.
Thus, the two required equalities are:
∠P = ∠Z and ∠R = ∠X
SAS CONGRUENCY CRITERION : SAS CONGRUENCY CRITERION
SAS CONGRUENCY CRITERION : SAS CONGRUENCY CRITERION Two triangles are said to be congruent, if two sides and the included angle of a triangle are equal to the corresponding sides and the included angle of the other triangle
PROBLEM : PROBLEM Q.C.1 Consider the given figure.
With respect to the given figure, answer the following question:
(a) Is ΔABC ≅ ΔDCB? Give reasons.
Solution of Q.C.1 : Solution of Q.C.1 In ΔABC and ΔDCB,
∠ABC = ∠DCB = 90° (Given)
AB = DC (Given)
BC = CB (Common sides)
∴ ΔABC ≅ ΔDCB (By SAS congruency criterion)
RHS CONGRUENCY CRITERION : RHS CONGRUENCY CRITERION
RHS CONGRUENCY CRITERION : RHS CONGRUENCY CRITERION Two right-angled triangles are said to be congruent under a correspondence if the hypotenuse and one side of one right-angled triangle is equal to the hypotenuse and one side of the other right-angled triangle.
PROBLEM : PROBLEM Q.D.1 ARE THE GIVEN TRIANGLES CONGRUENT OR NOT? JUSTIFY THE ANSWER.
SOLUTION OF Q.D.1 : SOLUTION OF Q.D.1 In ΔABC and ΔPQR,
Since ∠B = ∠Q = 90°,
AC = PR = 5 cm and BC = QR = 4 cm
Hence, ΔABC ≅ ΔPQR (By RHS congruency criterion)
Slide 23 : THE END