Grade 10 prove the angle in a semicircle theorem two ways with GeoGebra and Padlet

Grade 10 (Year 11, age 15 to 16) · 50 min · 1 device per student

The teacher sets the theorem that the angle in a semicircle is a right angle. Students construct a circle, a diameter and a point on the circumference in GeoGebra, measure the angle and drag the point around to check that it stays at 90°. They then write a proof in their books, either by drawing the radius to the point and using the two isosceles triangles, or by using the theorem that the angle at the centre is twice the angle at the circumference. Each student posts a photo of their written proof beside a screenshot of their construction in the Padlet column for their method. The teacher projects one strong proof of each kind and asks students to explain which facts each step depends on.

Why this is Interactive Amplify

Students construct, test and prove a given theorem, responding to a set problem with a known result. GeoGebra and Padlet amplify the usual proof lesson: dragging the construction tests the claim for every position of the point before students prove it, and the Padlet columns put every proof on one wall so the class compares the two methods.

Compared with

Drawing one diagram with compasses and a protractor and writing the proof in exercise books.

Watch out

If students formed and proved their own conjecture from the GeoGebra construction, the proof would be their own knowledge product and the lesson would be Creative.

Tools: GeoGebra, Padlet Nine ideas for your own version in Generate

This page is one of a growing set of PICRAT examples by cell, subject and grade. Page maintained by Andy Perryer.

Grade 10 prove the angle in a semicircle theorem two ways with GeoGebra and Padlet.

Nine ideas for your own version.

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Nine ideas for your own version.