wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Consider the following statements relating to the congruency of two right-angled triangles.

I. Equality of two sides of one triangle with some two sides of the second makes the triangles congruent.

II. Equality of the hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangles congruent.

III. Equality of the hypotenuse and an acute angle of one triangle with the hypotenuse and an angle of the second respectively makes the triangles congruent.

Which of the above statements are true?


A

I, II and III

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

I and II only

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

I and III only

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

II and III only

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

II and III only


According to RHS congruence rule, “In two right-angled triangles, if the length of the hypotenuse and one side of the triangle is equal to the length of the hypotenuse and the corresponding side of the other triangle, then the two triangles are congruent”.

I. Equality of two sides of one triangle with some two sides of the second makes the SS congruency, which is not valid.

II. Equality of the hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangles congruent by the RHS congruence rule.

III.Both triangles are right-angled triangles, so one angle is 90° in each.

Also given that the hypotenuse and an acute angle of one triangle are equal to the hypotenuse and an angle of the second respectively.

Thus, It makes the triangles congruent by the AAS congruence rule.

Hence, the correct statements are II and III only.


flag
Suggest Corrections
thumbs-up
1
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
RHS
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon