Practice Problems on RHS Congruence Rule

Problem 1: Triangle ABC has a right angle at B, where AB = 10, BC = 24, and AC = 26. Triangle DEF has a right angle at E, where DE = 10 and DF = 26. Are the two triangles congruent?

Problem 2: Triangle PQR has a right angle at Q, where PQ = 15, QR = 20, and PR = 25. Triangle XYZ has a right angle at Y, where XY = 20 and XZ = 25. Are the two triangles congruent?

Problem 3: Triangle LMN has a right angle at M, where LM = 9, MN = 12, and LN = 15. Triangle STU has a right angle at T, where ST = 9 and SU = 15. Are the two triangles congruent?

Problem 4: Triangle JKL has a right angle at J, where JK = 8, JL = 17, and KL = 15. Triangle VWX has a right angle at V, where VW = 8 and VX = 15. Are the two triangles congruent?

RHS Congruence Rule is also known as the HL (Hypotenuse-Leg) Congruence Theorem. It states the criteria for any two right-angle triangles to be congruent.

This rule states that if in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one corresponding side of the other triangle, then the triangles are congruent. In this article, we will discuss the criteria of congruence of right-angle triangles in detail including proof and examples.