Three parallel lines and the angle bisector

Classroom activities

Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.

• Can These Numbers Be Right? Proportional Segments and the Angle Bisector Theorem — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets

  12 drawings, each with four numbers: three lines cut by two transversals, or a triangle with a segment from a corner. Students decide whether the marks make the numbers right, make them impossible, or say nothing at all.

• Which Way Round Does It Go? Proportional Segments and the Angle Bisector Theorem — Answer Maze 10–15 minutes · 4 sheets

  8 boxes on one page, each a drawing with three numbers and x: three parallel lines cut by two transversals, or a triangle with an angle bisector. The wrong answers are the two forms of the lesson's main mistake: comparing pieces crosswise, and pairing a piece with the side across from it. The row of box numbers at the foot is the check.

• True From the Marks Alone? Proportional Segments and the Angle Bisector Theorem — Mystery Picture 25–35 minutes · 4 sheets

  25 squares, each one equation about one of four lettered figures: parallel lines with and without arrowheads, a triangle with an angle bisector and the same triangle with a median. Is the equation always true? Fill it or leave it white, and a picture appears.

• Which Pieces Make the Proportion? Proportional Segments and the Angle Bisector Theorem — Scavenger Hunt a full class period · 13 sheets

  16 cards around the room. Each has three parallel lines cut by two transversals, or a triangle with an angle bisector, three lengths and x. Pairing the pieces the wrong way round lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.