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If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
The first six books of the Elements of Euclid, with numerous exercises - Σελίδα 13
των Euclides - 1853 - 147 σελίδες
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1882 - 266 σελίδες
...the alternate angles EAD, ADC are equal, EF is parallel (I. 25) to BC. Proposition 30. Theorcm. — If one side of a triangle be produced, the exterior angle is equal to the two opposite interior angles; and the three interior angles of any triangle are equal...

The Practical Teacher, Τόμος 2

1883
...equal to the angle contained by the two lides equal to them of the other. See Prop. VIII. Bk. I. 3. If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. See Prop. XVI. Bk. I. 20 [MARCH, 1882. Music. A quarter of an hour allmved far this Paptr. i. Write,...

Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 96 σελίδες
...equal. 35. The bisectors of two opposite vertical angles are in the same straight line. PROP. 16. THEOR. If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. Given ABAC, having BC produced to D. To prove L. ACD > either i. A or L. ABC. Bisect AC at E (/. 10)....

The Practical Teacher; with which is Incorporated the Practical ..., Τόμος 2

Joseph Hughes - 1883
...equal to the angle contained by the two sides equal to them of the other. See Prop. VIII. Bk. I. 3. If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. See Prop. XVI. Bk. I. THE PRACTICAL TEACHER. [MARCH, 1882. Music. A quarter of an h«ur allowed for...

Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...Superposition.] COR. If a triangle is equiangular, it is also equilateral. THEOR. 9. If any side of a triangle is produced, the exterior angle is greater than either of the interior opposite angles. THEOR. 10. Any two angles of a triangle are together less than two right angles. COR. 1. If a triangle...

The Elements of Euclid: For the Use of Schools and Colleges; Comprising the ...

Euclid - 1883
...number of straight lines meeting at one point, are together equal to four right angles. PROPOSITION 16. THEOREM. If one side of a triangle be produced, the exterior angle shall be greater than either of the interior opposite angles. Let ABC be a triangle, and let one side...

Annual Report

1886
...Given 2x*—5x = 12, to find x. EUCLID. FIRST DIVISION. 1. Define a right angle, a circle, a square. 2. If one side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of any triangle are together...

An introduction to geometry, consisting of Euclid's Elements, book ..., Τόμος 1

Euclides - 1884
...greater than the angle A . 10. In the same figure, prove that the angle F is less than the angle ABC. 52. PROPOSITION XVI. — THEOREM. If one side of a triangle...greater than either of the interior opposite angles. Let ABC be a triangle whose side BC is produced to D. Then the exterior angle ACD shall be greater than...

Relfe brothers' Euclid sheets, propositions 1-26, book 1

Euclides - 1884
...SHEETS. PROPOSITIONS 1—26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS. PEOPOSITION XVI. If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. Let be a triangle, and let the side be produced to Then the exterior angle shall be greater than either...

The Civil service year book and official calendar

1884
...direct and an indirect demonstration. Define adjacent angles, opposite angles, and alternate angles. Z. If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. Prove, without producing a side, that the three angles of any triangle are equal to two right angles....