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 :
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 )
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 )