Mathematics & English The 1st sign of equality of triangles Theorem on equality of triangles If 2 sides and the angle between them of the same triangle are accordingly equal to 2 sides and the angle between them of the other triangle, then these triangles are equal. B A C B1 A1 C1 Given: AB is equal to A1B1 AC is equal to A1C1 The angle A is equal to the angle A1 To be to prove that: The triangle ABC is equal to the triangle A1B1C1 B A C B1 A1 C1 Proof As the angle A is equal to the angle A1 then the triangle ABC can be put on the triangle A1B1C1 so that the apex A will be superposed with the apex A1, and the sides AB and AC will be accordingly put on the rays A1B1 and A1C1. As far as, AB is equal to A1B1, AC is equal to A1C1, then the side AB will be superposed with the side A1B1 and the side AC with A1C1. In particular the points B and B1, C and C1 will be superposed. Therefore, the sides BC and B1C1 will be superposed. So the triangles ABC and A1B1C1 will be completely superposed. That means they are equal. The theorem has been proved. 1. To proof the equality of the triangles AOB and COD D Proof: A 1) AO is equal to OC ( according to the condition) 2) BO is equal to OD (according to the condition) 3) The angle AOB is equal to the triangle COD ( as vertical angles) O B C Therefore the triangle AOB is equal to the COD (according to the first sing of triangles). 2. To proof the equality of the triangles AOB and A C COD K B O D P Proof: 1)BA is equal to CD ( according to the condition ) 2) BO is equal to OD ( according to the condition ) 3)The angle ABО is equal to the angle CDO (as their adjacent angles are equal ) Therefore the triangle AOB is equal to the triangle COD ( according to the first sign of equality of triangles). • The presentation has been done by: Mikhail Verbitskiy, Yana Karasyova, 7A form, school №511 • L.I. Kunaeva, Maths teacher • V.V. Klyueva, English teacher Moscow 2011 Библиография 1. Атанасян, Л.С. Геометрия: Учеб. для 7-9 кл. сред. школы [Текст]/ Л.С. Атанасян, В.Ф. Бутузов, С.Б. Кадомцев и др. – М.: Просвещение; ОАО «Моск. учебн.» 2006. – 384с. 2. Рабинович, Е.М. Задачи и упражнения на готовых чертежах. 7-9 классы. Геометрия [Текст]/ Е.М. Рабинович. – М.:Илекса, 2006.-60с. Подготовили: • Ученики 7 «А» класса ГОУ СОШ № 511 Вербицкий Михаил и Карасева Яна • Учитель математики: Кунаева Л.И. • Учитель английского языка: Клюева В.В.