If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent. State whether the statement is true or false.
Solution:
Given, if two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent.
We have to determine if the given statement is true or false.
Consider two right angle triangles ABC and XYZ,
According to the question,
AB = 5 cm; BC = 4cm and ∠B = 90°
XY = 5 cm; YZ = 4 cm and ∠Y = 90°
The SAS criterion states that If two sides of one triangle are respectively proportional to two corresponding sides of another, and if the included angles are equal, then the two triangles are congruent.
By SAS rule, ∆ABC ≅ ∆XYZ
Therefore, two right angled triangles ABC and XYZ are congruent.
✦ Try This: If the base and hypotenuse of a right triangle are equal to the base and hypotenuse of another right triangle, then the right 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 99
If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent. State whether the statement is true or false.
Summary:
The given statement,”If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent” is true.
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