Congruent triangles: match the corners first
Two congruent triangles are drawn, and the statement names them with their corners in matching order: △ABC ≅ △MKL means A matches M, B matches K and C matches L. One triangle has its sides or its angles marked. The other is drawn turned round or flipped over, with one side or angle marked with a question mark, and the student types its length or size.
The picture is the trap. Once a triangle is turned or flipped, the matching side is rarely in the same place, so the student has to go by the letters, not by where things are drawn. In some questions only two sides and the perimeter, or two of the angles, are given, and the part asked for often matches the one that is not marked: it has to be worked out first, from the perimeter or from the angles adding up to 180°. The working colours matching corners alike, lights up the asked part and its match, and writes in the answer.
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What changes each time
- Sides or angles: sides are whole numbers from 3 to 30 in cm, m or mm, angles are whole degrees from 30° to 110°, and every triangle has three different sides
- All three sides or angles marked, or only two (with the perimeter for sides), so the matching part may need working out first
- The copy turned round or flipped over and stood any way up, with new letters and a new matching order each time
More shapes and angles practice
- Sides and corners of 2D shapes (Grade 2)
- Faces, edges and vertices (Grade 3)
- Sorting quadrilaterals (Grade 3)
- Turning and flipping letters (Grade 3)
- Counting squares of every size (Grade 3)
- Inside or outside the loop (Grade 3)
- Which piece fills the gap? (Grade 3)
- Symmetry on a grid (Grade 4)
- Rotations and reflections (Grade 4)
- Reading a protractor (Grade 4)
- Parallel and perpendicular lines (Grade 4)
- Parts of a circle (Grade 4)
- Draw without lifting your pencil (Grade 4)
- Can these sticks make a triangle? (Grade 4)
- Lines, rays and line segments (Grade 4)
- Counting line segments (Grade 4)
- Triangle from two circles (Grade 4)
- Splitting an angle in half (Grade 4)
- 3D shapes: side view (Grade 5)
- Rectangle in a quarter circle (Grade 5)
- Painted cube puzzle (Grade 5)
- Rope around the Earth (Grade 5)
- Can dominoes cover the board? (Grade 5)
- Most crossing points of straight lines (Grade 5)
- Equal radii: find the missing length (Grade 5)
- Angles in a circle (Grade 6)
- Vertically opposite angles (Grade 6)
- Inscribed circle in a right triangle (Grade 8)
- SSS and SAS: is it enough to prove congruence? (Grade 8)