How to know the two triangles are congruent and when to use the axioms and on which triangle?

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Solution

1. SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

2. SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

3. ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.
If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

4. RHS congruence: It means we have two right-angled triangles with the same length of hypotenuse and
the same length for one of the other two legs.

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Question 7
Draw a $Δ A B C$ in which $A B$ = $4$ cm, $B C$ = $6$ cm and $A C$ = $9$ cm, construct a triangle similar to $Δ A B C$ with scale factor $\frac{3}{2}$ . Justify the construction. Are the two triangles congruent? Note that, all the three angles and two sides of the two triangles are equal.

Solution

Thinking process

Triangles are congruent when all corresponding sides and interior angles are congruent The triangles will have the same shape and size, but one may be a mirror image of the other.

So, first, we construct a triangle similar to $Δ A B C$ with scale factor $\frac{3}{2}$ and use the above concept to check the triangles are congruent or not.

Q. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Q. In triangles ABC and DEF, AB

=

FD and

∠ A = ∠ D

. The two triangles will be congruent by
SAS axiom if :

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