If two triangles (ABC, DEF) have two sides (AB, AC) of one respectively equal to two sides (DE, DF) of the other, but the base (BC) of one greater than the base (EF) of the other, the angle (A) contained by the sides of that which has the greater base is greater them the angle (D) contained by the sides of the other.
If two triangles (ABC, DEF) have two sides (AB, AC) of one respectively equal to two sides (DE, DF) of the other, but the contained angle (BAC) of one greater than the contained angle (EDF) of the other, the base of that which has the greater angle is greater than the base of the other.
At a given point (A) in a given right line (AB) to make an angle equal to a given rectilineal angle (DEF)
To construct a triangle which three sides shall be respectively equal to three given lines $(A, B, C)$, the sum of every two of which is greater than the third.
If two lines $(BD, CD)$ be drawn to a point $(D)$ within a triangle from the extremities of its base $(BD)$, their sum is less than the sum of the remaining sides $(BA, CA)$, but they contain a greater angle.
The sum of any two sides $(BA, AC)$ of a triangle $(\triangle ABC)$ is greater than the third.
If one angle $(\angle B)$ of a triangle $(\triangle ABC)$ be greater than another angle $(\angle C)$, the side (AC) which it opposite to the greater angle is greater than the side $(AB)$ which is opposite to the less.
If in any triangle $(\triangle ABC)$ one side $(AC)$ be greater than another $(AB)$, the angle opposite to the greater side is greater than the angle opposite to the less.
Any two angles $(\angle B, \angle C)$ of a triangle $(\triangle ABC)$ are together less than two right angles.
If any side $(BC)$ of a triangle $(\triangle ABC)$ be produced, the exterior angle $(\angle ACD)$ is greater than either of the interior non-adjacent angles.
If Two right lines $(AB, CD)$ intersect one another, the opposite angles are equal $(CEA=DEB$, and $BEC=AED)$
If at a point $(B)$ in a right line $(BA)$ two other right lines $(CB, BD)$ on opposite sides make the adjacent angles $(\angle CBA, \angle ABD)$ together equal to two right angles, these two right lines form one continuous line.
The adjacent angles $(\angle ABC, \angle ABD)$ which one right lines $(AB)$ standing on another $(CD)$ makes with it are either both right angles, or their sum is equal to two right angles.
To draw a perpendicular to a given indefinite right line $(AB)$ from a given point $(C)$ without it.
From a given point $(C)$ in a given right line $(AB)$ to draw a right line perpendicular to the given line.
To bisect a given finite right line $(AB)$.
To bisect a given rectilineal angle $(\angle BAC)$.
If two triangles $(\triangle ABC, \triangle DEF)$ have two sides $(AB, AC)$ of one respectively equal to two sides $(DE, DF)$ of the other, and have also the base $(BC)$ of one equal to the base $(EF)$ of the other; then the two triangles shall be respectively equal to the angles of the – namely, those shall be equal to which the equal sides are opposite.
If two triangles $(\triangle ACB, \triangle ADB)$ on the same base $(AB)$ and on the same side of it have one pair of conterminous sides $(AC, AD)$ equal to one another, the other pair of conterminous sides $(BC, BD)$ must be unequal.
If two angles $(\angle B, \angle C)$ of a triangle be equal, the sides $(AC, AB)$ opposite to them are also equal.
