Question

Decide whether the SSS congruence is true with the following figure. Give reasons.

Answer 1

Hint: Here, in the given question, we are given a figure of quadrilateral consisting of two triangles and also, measurements of sides are given. And we are asked to check whether the SSS congruence is true or not and support the answer by stating the reason. For this, we will check if all the sides are equal to both the triangles, then the two triangles will be SSS congruent, otherwise not.

Complete step-by-step solution:
Two figures having the same shape and size are called congruent figures. Or we can say that, the two triangles are congruent if each one when superimposed on the other covers the other exactly.
Side-Side-Side (SSS) congruence rule: Two triangles are congruent, if the three sides of one triangle are equal to corresponding sides of the other triangle.
Now, to check whether the given figure is SSS congruent or not, let us compare the sides of the two triangles.
In\[\vartriangle ADL\] and \[\vartriangle SDL\],
\[LD = LD\] (same side)
\[SD = AL\] (both measuring \[4\]units)
\[AD \ne SL\] (one measuring \[2.5\] units and other \[3\]units)
Here, only two corresponding sides are equal.
Hence, the given figure is not SSS congruent.

Note: When we have to prove two triangles congruent, we use some congruent conditions to prove. One of them is the side-side-side congruence rule as we have discussed above. The other three are:
Side-angle-side (SAS) congruence rule: This states that if two sides and the included angle of the one triangle are equal to corresponding sides and equal to another triangle, then two triangles will be congruent.
Angle-side-angle (ASA) congruence rule: This states that two triangles will be congruent if two angles and the included side of one triangle is equal to corresponding angles and sides of another triangle.
Right-angle-Hypotenuse (RHS) congruence rule: This states that two right triangles will be congruent, if the hypotenuse and one side of the triangle is equal to the corresponding angle and side of another triangle.