The RHS Construction
Base QR, the perpendicular at Q, and the 5 cm arc from R.
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The right angle ensures the second intersection forms a perfectly reflected, congruent triangle.
The one case where two sides and a non-included angle do work, right triangles (RHS), and all five rules together.
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One special case where two sides and a non-included angle do work.
We previously saw that the SSA condition (two sides and a non-included angle) does not guarantee congruence for triangles in general. However, there are some special cases when SSA DOES guarantee congruence, and here is one important case.
Four steps that build the 4 cm, 90 degree, 5 cm triangle.
Construct a right-angled triangle with base , a right angle at , and hypotenuse . Check if all triangles with these measurements are congruent.
Base QR, the perpendicular at Q, and the 5 cm arc from R.
The right angle ensures the second intersection forms a perfectly reflected, congruent triangle.
The RHS test and the meaning of hypotenuse.
A special case that guarantees congruence.
Applies only when both triangles contain a right angle. The equal hypotenuse pair must be identified correctly. The HYPOTENUSE is the side opposite the right angle, and it is the longest side of a right-angled triangle. (Units: cm for sides, degrees for angles)
If a triangle has at B, a hypotenuse of , and another side of , any other triangle with these exact measurements will be perfectly congruent to it.
Complete the statement of the RHS condition and its vocabulary.
In a right-angled triangle, the side opposite the right angle is called the . When checking for congruence, RHS stands for Right Side. The RHS rule applies only when both triangles contain an angle of degrees. Besides the right angle, RHS needs the and one other to be equal. Without a right angle, two sides and a non-included angle form the case, which does not guarantee congruence.
Four right-triangle cases to test against the RHS requirements.
Two right-angled triangles have equal hypotenuses of and one pair of equal legs of . Are they congruent?