المثلثات المتشابهة - الصف الأول الثانوي

المثلثات المتشابهة

• Defined as triangles with equal corresponding angles and proportional corresponding sides.

خواص المثلثات المتشابهة

• If the angles of two triangles are equal, the corresponding sides are proportional.
• The ratio of corresponding sides is equal to the ratio of the corresponding sides of the other triangle.

حل مشكلات الارتفاعات والأبعद في المثلثات والأشكال الهندسية الأخرى

• Using the properties of similar triangles, we can solve problems related to heights and dimensions in triangles and other geometric shapes.
• Examples include calculating the height of a pyramid or a tower.

إثبات المثلثات المتشابهة

• We can prove that two triangles are similar using the following steps:
  • Show that the corresponding angles are equal.
  • Show that the corresponding sides are proportional.
  • Use the ratio of corresponding sides to find the length of the unknown side.

تطبيقات المثلثات المتشابهة

• Similar triangles can be used to calculate unknown distances or dimensions in large triangles, such as pyramids or towers.
• The ratio of corresponding sides can be used to find the length of the unknown side.

exemples

• If the ratio of corresponding sides is 1:2, and the length of the shorter side is 3 cm and 4 cm, the length of the corresponding side in the larger triangle is 6 cm and 8 cm.
• If the ratio of corresponding sides is 3:4, and the length of the shorter side is 8 cm, the length of the corresponding side in the larger triangle is 10.67 cm.