Triangles Mind Map

Two triangles are similar when their corresponding angles are equal and their corresponding sides are in the same ratio.

Write the corresponding vertices in the same order before checking angles or side ratios.

If three angles of one triangle are respectively equal to three angles of another triangle, the triangles are similar.

If two corresponding angles match, the third one will also match because the total is always 180°.

Two triangles are similar if one included angle is equal and the two sides around that angle are proportional.

Check the angle that lies between the two sides you are comparing.

Two triangles are similar if all three corresponding sides are proportional.

Always compare sides in matching order before concluding SSS similarity.

A line drawn parallel to one side of a triangle divides the other two sides in the same ratio.

First check the parallel mark, then write the ratio of the two cut sides carefully.

If a line divides two sides of a triangle in the same ratio, then the line is parallel to the third side.

Look for equal ratios on the two sides that are cut by the same line.

For similar triangles, the ratio of their areas equals the square of the ratio of their corresponding sides.

Find the side ratio first, then square both terms carefully.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

First identify the right angle and the longest side before writing the formula.

If the square of the longest side of a triangle equals the sum of the squares of the other two sides, the triangle is right-angled.

Always start with the longest side when using the converse.

In a right triangle, the altitude from the right angle to the hypotenuse creates two smaller triangles that are similar to the original triangle and to each other.

Label the two parts of the hypotenuse before using h² = pq.

Once two triangles are proved similar, you can use corresponding side ratios and equal angles to prove lengths, proportions, and parallel-line results.

After proving similarity, write only matching side ratios and keep the vertex order correct.

The scale factor is the number by which one similar triangle is enlarged or reduced to get the other.

Decide first whether you are moving from the smaller triangle to the larger one or the other way around.