The exterior angle, sides and angles, right triangles
See that an exterior angle equals the sum of two interior angles, that the larger angle lies opposite the longer side, and use the congruence criteria of right triangles.
- Ukraine: grade 7
Guide
Ukrainian Geometry 7 (§§ 10, 16, 17, 18) teaches these: criteria for an isosceles triangle, the exterior angle, sides against angles, and congruence of right triangles.
An exterior angle of a triangle is the angle next to an interior angle (supplementary to it). It equals the sum of the two interior angles not next to it, so it is larger than each of them.
In a triangle the larger angle lies opposite the longer side, and the other way round. So if two angles of a triangle are equal, it is isosceles.
Right triangles are congruent by: two legs; a leg and an acute angle; the hypotenuse and an acute angle; the hypotenuse and a leg.
Drag the vertices and watch the numbers under the figure.