SSS and SAS: is it enough to prove congruence?
Two triangles are drawn, the second turned round or flipped over, with some sides and angles marked equal on both and listed in the question. The student chooses the rule that proves the triangles are congruent, SSS or SAS, or says the marks are not enough information.
The trap is two sides and an angle. That is SAS only when the angle sits between the two marked sides, where they meet. When it is at another corner, two different triangles can fit the same marks, and the working shows both by swinging the third corner to its second place. Three equal angles are not enough either: a smaller copy has the same angles. The working colours each marked pair and lights up the parts that decide the rule.
Numbers&Me is free. Sign up to practise more, or set it as homework in under a minute, and it marks itself.
What changes each time
- Four kinds of marking: all three sides, two sides with the angle between them, two sides with an angle at another corner, or all three angles
- Sides are different whole numbers from 3 to 20 in cm, m or mm, and angles whole degrees; the marked angle can be at any corner
- The second triangle 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)
- Congruent triangles: match the corners first (Grade 6)
- Vertically opposite angles (Grade 6)
- Inscribed circle in a right triangle (Grade 8)