**Construction & Conjecture - Triangle**

1) Lines *AB*, *BC* and *CA* of triangle *ABC* have been rotated through the same (blue) angle *DEF*, respectively around *B*, *C* and *A* as shown.

2) What do you notice about triangles *ABC* and *GHI*? Check your conjecture by clicking on the '*Show Angle Measurements GHI*' button.

3) Check your conjecture further by dragging points *A*, *B* or *C* to change triangle *ABC*, or *F* to change the angle of rotation.

**Challenge**

4) Can you explain why (prove) that triangles *ABC* and *GHI* are similar?

5) Formulate a converse and investigate. If true, explain why (prove) or if false, give a counter-example.

Rotated Lines

**Construction & Conjecture - Quadrilateral**

1) Investigate what happens if the same construction as for a triangle is carried out with a quadrilateral.

(Think about it before clicking on the '*Link to quadrilateral*' button on the bottom right of the sketch).

2) What do you notice about quadrilaterals *ABCD* and *KLMN*? Are they still similar?

3) Click on the 'Show Ratio measurements' button to check your observation above. What do you notice about the ratios of the corresponding sides? What does this tell you?

4) Click on the '*Show Angle Measurements KLMN*' to show the angles of *KLMN*. What do you notice? Formulate a conjecture.

5) Firther check your conjecture by dragging points *A*, *B*, *C* or *D* to change quadrilateral *ABCD*, or *G* to change the angle of rotation.

**Challenge**

6) Can you explain why (prove that) your observations above are true?

7) Formulate a converse and investigate. If true, explain why (prove) or if false, give a counter-example.

**Generalize Further**

Can you generalize further to pentagons, hexagons, etc.? What happens if the lines *AB*, *BC* and *CA* are rotated through the same angle around points other than the vertices?

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Release: 2020Q2, Semantic Version: 4.6.2, Build Number: 1047, Build Stamp: 139b185f240a/20200428221100

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Created 17 Nov 2007 by Michael de Villiers; updated to *WebSketchpad*, 27 August 2022.