SAS Congruence

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2017-04-27 11:05

This example illustrates the SAS Congruence Theorem, which states that if two triangles have two sides and the included angle equal, then the triangles are congruent. By rotating and constructing segments, we can visually understand this theorem. The example uses Circle, Line, Intersect, Segment, Rotate, Angle, etc., GeoGebra commands. Suitable for middle and high school students to learn about triangle congruence.

GeoGebra Commands & Parameters

Circle(A, a) → c
Line(A, B) → f
Intersect(c, f) → C, D
Segment(A, D) → g
Rotate(A, α, D) → A'
Angle(A, D, A') → β
Circle(D, b) → d
Line(D, A') → h
Circle(D, b) → e
Intersect(e, h) → E, F
Segment(D, F) → i
Segment(A, F) → j
Circle(G, a) → k
Line(G, H) → l
Intersect(k, l) → I, J
Segment(G, J) → m
Rotate(G, α, J) → G'
Angle(G, J, G') → γ
Line(J, G') → n
Circle(J, b) → p
Intersect(p, n) → K, L
Segment(J, L) → q
Segment(L, G) → r

AI Drawing Prompt Reference

Draw two triangles to illustrate the SAS congruence theorem. Start with one triangle, having a base side, then at one endpoint of the base construct an angle of a given measure, and along the other side of that angle mark off a segment of a given length, then connect to form the first triangle. Next, from a different starting point, draw a segment equal in length to the base, construct the same angle at one endpoint, and mark off the same second side length, then connect to form the second triangle. The two triangles should have two corresponding sides equal and the included angle equal, visually showing they are congruent.

The prompt above was compiled from the original drawing commands and is for reference only.