If hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent. State whether the statement is true or false.
Solution:
Given, if hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent.
We have to determine if the given statement is true or false.
Consider two right angled triangles ABC and PQR,
According to the question,
∠B = ∠Q = 90°
The acute angles, ∠C = ∠R
We know that if the two angles of a triangle are equal to the two angles of another triangle then the third angle will also be equal.
So, ∠A = ∠P
ASA congruence criterion states that, "if two angles of one triangle, and the side contained between these two angles, are respectively equal to two angles of another triangle and the side contained between them, then the two triangles will be congruent".
From the figure,
∠C = ∠R
AC = PR
∠A = ∠P
By ASA rule, ∆ABC ≅ ∆PQR
✦ Try This: If hypotenuse and the side of one right triangle are equal to the hypotenuse and the corresponding side of another right triangle, then the triangles are congruent. State whether the statement is true or false.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 104
If hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent. State whether the statement is true or false.
Summary:
The given statement,”If hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent” is true.
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