In Fig. 6.28, two triangles are congruent by RHS. State whether the statement is true or false.
Solution:
Given, two triangles are congruent by RHS.
We have to determine if the given statement is true or false.
According to Pythagorean theorem,
Hypotenuse² = Perpendicular² + Base²
Considering triangle ABC,
AC² = AB² + BC²
AC² = 4² + 5²
AC² = 16 + 25
AC² = 41
Taking square root,
AC = √41 cm
Considering triangle PQR,
PR² = PQ² + RQ²
PR² = 4² + 5²
PR² = 16 + 25
PR² = 41
Taking square root,
PR = √41 cm
RHS congruence theorem states that, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, the two triangles are congruent.
By RHS rule, ∆ABC ≅ ∆PQR
Therefore, the two triangles are congruent.
✦ Try This: In Fig, two triangles are congruent by ASA. 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 86
In Fig. 6.28, two triangles are congruent by RHS. State whether the statement is true or false.
Summary:
The given statement,”In Fig. 6.28, two triangles are congruent by RHS” is true.
☛ Related Questions:
- A right-angled triangle may have all sides equal. State whether the statement is true or false.
- If two angles of a triangle are equal, the third angle is also equal to each of the other two angles . . . .
- The congruent figures super impose each other completely. State whether the statement is true or fal . . . .