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Hypotenuse–Leg Congruency Rule for Right Triangles

Hypotenuse–Leg Congruency Rule for Right Triangles
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2020-08-16 20:58
TriangleCircleAngleGeometric Construction
This GeoGebra example demonstrates the hypotenuse–leg (HL) congruency principle: when two right triangles have equal hypotenuse and one corresponding leg, the triangles can be proven congruent. It focuses on right triangles, congruency criteria (HL rule), and how corresponding sides and angles align under the given constraints. The construction is carried out using GeoGebra commands such as Segment (building triangle sides), Point (defining key vertices/points), Angle (marking or constraining angles, including the right angle), Circle and Intersect (creating loci of points with required distances and computing their intersections), and Rotate (moving/aligning the configuration to compare corresponding elements). The setup is well-suited for classroom demonstrations, homework, and self-study in geometry for explaining and visualizing the HL congruency theorem.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Angle(C, B, A) → α
  4. Segment(C, A) → h
  5. Point(Circle[D, g]) → E
  6. Segment(D, E) → i
  7. Rotate(E, α, D) → E'
  8. Angle(E, D, E') → β
  9. Circle(D, f) → c
  10. Circle(E, h) → d
  11. Intersect(d, c) → F, G, ,
  12. Segment(D, G) → j
  13. Segment(E, G) → k

AI Drawing Prompt Reference

Draw two right triangles to illustrate the hypotenuse-leg congruence rule. Start with one right triangle, marking its right angle)Skip, and note the lengths of its hypotenuse and one leg. Then, from another point, construct a segment equal to that leg, and rotate it by the same right angle to form the second triangle's leg. Next, draw a circle centered at the second triangle's right-angle vertex with radius equal to the first hypotenuse, and another circle centered at the other known vertex with radius equal to the first triangle's other leg. The intersection of these circles gives the third vertex. Connect this vertex to the two known points to complete the second triangle, and label the corresponding equal sides and angles.
The prompt above was compiled from the original drawing commands and is for reference only.