Altitudes and the orthocenter
- Where the closest point goes — 3 tasks
- Vertex, right angle, or both — 3 tasks
- The far end of an altitude — 3 tasks
- Where the three altitudes cross — 3 tasks
- Going Deeper — 6 tasks
- Practice — 27 tasks
- Summary — 2 tasks
- Cool-down — 3 tasks
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.
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Altitude, Median, or Neither? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 scalene triangles ABC, each with one thick segment and its marks (right-angle squares, tick marks), sorted into "the altitude to side BC", "the median to side BC" and "neither". Half the pieces draw the altitude and the median together, one thick and one thin. The last row holds a perpendicular bisector, an altitude to a different side, a segment with no marks, and a segment in a right triangle whose altitude to BC is a leg.
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Where Do the Altitudes Meet? — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a short question about an altitude: the area when a median or a slanted side is printed beside the height, a height from an area, where the altitudes of an obtuse or a right triangle meet, and where an altitude lands outside a triangle. The wrong answers are the two mistakes this lesson exists to stop. The row of box numbers at the foot is the check.
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Is the Thick Segment an Altitude? Altitudes of a Triangle — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each a scalene triangle with one thick segment: fill the square only if the marks show it is an altitude (from a corner, square to the opposite side or its line). Altitudes outside obtuse triangles and legs of right triangles are filled; medians, perpendicular bisectors, rays and segments with the square in the wrong place stay white. When every square is right, a picture appears.
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Altitudes and the Orthocenter — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each asking a number that an altitude decides: an area when a slanted side or a median is printed beside the height, the height from the area, the height to a second side, and the x-coordinate of the orthocenter. Each card's common mistake lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.