In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

Open in App

Solution

It is given that

We are asked to show that

Let us assume

, and are right angled triangle.

Thus in and, we have

And (given)

Hence by AAs congruence criterion we haveProved.

Suggest Corrections

Similar questions

In two right triangles, one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

Q. In two right triangles one pair of acute angles and the sides opposite to them are equal. Prove that the triangles are congruent.

In two right triangles, one side and an acute angle of one are equal to the corresponding side and angle of the other, then ΔABC ΔDEF by the criterion

Q. Which of the following statements are true and which of them are false?

(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two figures have equal areas, they are congruent.
(iv) If two triangles are equal in area, they are congruent.
(v) If two sides and one angle of a triangle are equal to the corresponding two sides and angle of another triangle, the triangle are congruent.
(vi) If two angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent.
(vii) If three angles of a triangle are equal to the corresponding angles of another triangle then the triangles are congruent.
(viii) If the hypotenuse and an acute angle of a right triangle are equal to the hypotenuse and the corresponding acute angle of another right triangle then the triangle are congruent.
(ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.
(x) If two triangles are congruent then their corresponding sides and their corresponding angles are congruent.

Q. Prove that two triangles are congruent if any two sides and the
included angle of one triangle is equal to any two sides and the included angle of other triangle.

Join BYJU'S Learning Program

In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

It is given that We are asked to show that Let us assume , and are right angled triangle. Thus in and, we have And (given) Hence by AAs congruence criterion we haveProved.

It is given that

We are asked to show that

Let us assume

, and are right angled triangle.

Thus in and, we have

And (given)

Hence by AAs congruence criterion we haveProved.