Triangles having equal areas and having one side of one of the triangles, equal to one side of the other, have their corresponding altitudes equal.

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle.

If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle.

If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle.

Theorem 6.6 : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Theorem 6.4 : If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similiar

If two angles and a side of one triangles are equal to two angles and a side of another triangles , the triangles are congruent.

Two isosceles triangles have equal vertical angles. Show that the triangles are similar. If the ratio between the areas of these two triangles is 16 : 25, find the ratio between their corresponding altitudes.

The area of a triangle is equal to that of a square whose each side measures 60 metres. Find the side of the triangle whose corresponding altitude is 90 metres.

Is it true to say that, if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reason for your answer.