Proof
Superpose one triangle on the other; corresponding sides and angles
coincide; by Common Notion 4 the figures are equal.
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Required by (dependents) (25)
- I.5Proposition I.5In isosceles triangles the angles at the base are equal to one another; and if the equal straight lines be produced…
- I.6Proposition I.6If in a triangle two angles are equal to one another, the sides which subtend the equal angles will also be equal to…
- I.10Proposition I.10To bisect a given finite straight line.
- I.16Proposition I.16In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and…
- I.24Proposition I.24If two triangles have the two sides equal to two sides respectively, but have the one of the angles contained by the…
- I.25Proposition I.25If two triangles have the two sides equal to two sides respectively, but have the one base greater than the other, they…
- I.26Proposition I.26If two triangles have the two angles equal to two angles respectively, and one side equal to one side, namely either…
- I.33Proposition I.33The straight lines joining equal and parallel straight lines (at the extremities which are in the same directions) are…
- I.35Proposition I.35Parallelograms which are on the same base and in the same parallels are equal to one another.
- I.47Proposition I.47In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides…
- III.3Proposition III.3If in a circle a straight line through the centre bisect a straight line not through the centre, it also cuts it at…
- III.17Proposition III.17From a given point to draw a straight line touching a given circle.
- III.24Proposition III.24Similar segments of circles on equal straight lines are equal to one another.
- III.26Proposition III.26In equal circles equal angles stand on equal circumferences, whether they stand at the centres or at the circumferences.
- III.29Proposition III.29In equal circles equal circumferences are subtended by equal straight lines.
- III.30Proposition III.30To bisect a given arc.
- IV.5Proposition IV.5About a given triangle to circumscribe a circle.
- IV.6Proposition IV.6In a given circle to inscribe a square.
- IV.12Proposition IV.12About a given circle to circumscribe an equilateral and equiangular pentagon.
- IV.13Proposition IV.13In a given pentagon, which is equilateral and equiangular, to inscribe a circle.
- IV.14Proposition IV.14About a given pentagon, which is equilateral and equiangular, to circumscribe a circle.
- VI.6Proposition VI.6If two triangles have one angle equal to one angle and the sides about the equal angles proportional, the triangles…
- XI.4Proposition XI.4If a straight line be set up at right angles to two straight lines which cut one another, at their common point of…
- XI.20Proposition XI.20If a solid angle be contained by three plane angles, any two, taken together in any manner, are greater than the…
- XI.35Proposition XI.35If there be two equal plane angles, and on their vertices there be set up elevated straight lines containing equal…
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