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" If two triangles have an angle of one equal to an angle of the other... "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Σελίδα 172
των Euclid, Rev. John Allen - 1822 - 494 σελίδες
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Solid Geometry, Τόμοι 6-9

George Albert Wentworth - 1902 - 218 σελίδες
...products of their bases by their altitudes. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. 412. The areas of two similar polygons are...

Elementary Geometry: Plane

James McMahon - 1903 - 358 σελίδες
...Similarly, it may be proved that B"C" = B'C'. Two sides and included angle. 44. THEOREM 10. If two triangles have an angle of one equal to an angle of the other, and the sides about these angles proportional, then the triangles are similar. Let the triangles ABC...

Plane Geometry by the Suggestive Method

John Alton Avery - 1903 - 122 σελίδες
...triangle, a smaller triangle is formed similar to the given triangle. THEOREM V 164. If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. Hyp. In the A RST and R'S'T', let...

Mathematics, mechanics, heat

American School (Chicago, Ill.) - 1903
...A', and ^^_ = — — A. 1 1 ./Y li Therefore the triangles ABE and A' B' E' are similar, for they have an angle of one equal to an angle of the other, and the sides including these angles proportional (Theorem LIII). Again, since the polygons are similar,...

Solid Geometry

Fletcher Durell - 1904 - 206 σελίδες
...326. // two triangles have their homologous sides proportional they are similar. 327. // two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. 328. // two triangles have their sides...

Plane Geometry

Fletcher Durell - 1904 - 372 σελίδες
...is similar to A ABC). Art. 306. Art. 101. Ax. 8. QED PROPOSITION XVII. THEOREM 327. If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. Given the A ABC and A'B'C', in which...

Plane and Solid Geometry

George Albert Wentworth - 1904 - 473 σελίδες
...AREAS OF POLYGONS. PROPOSITION VII. THEOREM. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Let the triangles ABC and ADE have the common...

PLANE AND SOLID GEOMETRY

FLETCHER DURELL. PH.D. - 1911
...8. (/or its equal A AFH is similar to A ABC). QED PROPOSITION XVII. THEOREM 327. 7/ jfwo triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. A Given the A ABC and A'B'C', in which...

Catalogue ...

Yale University. Sheffield Scientific School - 1905
...hypotenuse of a similar triangle is 1o in. What is the area of the second triangle? 6. The areas of two triangles which have an angle of one equal to an angle of the other are to each other as the products of the sides including the equal angles. 7. When is a circle said to be the locus of...

School Science and Mathematics, Τόμος 22

1922
...and C; draw OD J.AC; since <B = <AOD, \ve may apply to AsABC and AOD the theorem: If two triangles have an angle of one equal to an angle of the other, the ratio of their areas equals the ratio of the products of the sides including this angle. Hence...




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