State TRUE or FALSE. If false , give reasons for that:

1 . If two traingles have their corresponding angles equal, then the traingles are congruent.

2. Any two right - angled traingles are congruent.

3. A 1 - rupee and a 5 - rupee coind are congruent.

4. If two traingles are congruent, their corresponfing angles are equal.

Answer :

we know triangle can be congruence according to these rules

1 ) SSS ( Side - Side - Side ) If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.

2 ) SAS ( Side - Angle - Side ) If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

3 ) ASA ( Angle - Side - Angle ) If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

4 ) AAS ( Angle - Angle - Side ) If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

4 ) RHL ( Right angle - Hypotenuse - Leg ) If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent.

So ,

we can see that in all five rules , we have to show three reason to prove any two triangle congruent to each other .

So, we can say we can't show congruency by just two reasons instead of three .

So,

1 . If two triangles have their corresponding angles equal, then the triangles are congruent. -

**False**( As we just know two reason , that is not sufficient as we discuss above )

2. Any two right - angled triangles are congruent. -

**False**( As here we know triangles are right angles but their sides could be any thing , so can't state that these are congruent )

3. A 1 - rupee and a 5 - rupee coin are congruent.

**- False**( As we know two circle can be congruent when they have equal radii ( as coin is in shape of circle ) but here we are not sure that both have same radii or not , So we can say both coins are not congruent )

4. If two triangles are congruent, their corresponding angles are equal. -

**True**( from CPCT ( corresponding parts of congruent triangles ) rule for congruent triangle , we know if any two triangles are congruent to each other , than their corresponding angles and sides equal to each other )

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