A right-angled triangle (RHS)
Construct △ABC, right-angled at B, with BC = 4 cm and the hypotenuse AC = 5 cm.
Construct △ABC, right-angled at B, with BC = 4.5 cm and the hypotenuse AC = 7 cm.
Construct △ABC, right-angled at B, with BC = 5 cm and the hypotenuse AC = 6.5 cm.
Construct △ABC, right-angled at B, with BC = 6 cm and the hypotenuse AC = 7.5 cm.
1. Draw BC = 4 cm.
2. At B, construct ∠CBX = 90°.
3. With C as the center and radius 5 cm, cut BX at A.
4. Join AC: △ABC is the triangle, right-angled at B.
1. Draw BC = 4.5 cm.
2. At B, construct ∠CBX = 90°.
3. With C as the center and radius 7 cm, cut BX at A.
4. Join AC: △ABC is the triangle, right-angled at B.
1. Draw BC = 5 cm.
2. At B, construct ∠CBX = 90°.
3. With C as the center and radius 6.5 cm, cut BX at A.
4. Join AC: △ABC is the triangle, right-angled at B.
1. Draw BC = 6 cm.
2. At B, construct ∠CBX = 90°.
3. With C as the center and radius 7.5 cm, cut BX at A.
4. Join AC: △ABC is the triangle, right-angled at B.
Why it works
The right angle at B fixes the line A is on, and the hypotenuse fixes how far A is from C: the arc cuts that line in one point above BC. Two right-angled triangles with the same hypotenuse and the same side are congruent (RHS).