Corresponding angles are always equal

Alternate angles are always equal

If two triangles are congrent , then the corresponding angles are equal

Is the following statement true? Why? "Two quadrilaterals are similar, if their corresponding angles are equal".

Theorem 6.3 : If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

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

Corresponding angles between parallel lines are equal

In the given figure, line l || m and n is a transversal. If /_1=40^0, find all the angles and check that all corresponding angles and alternate angles are equal.

Read the following statements which are taken as axioms (i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal. (ii) If a transversal intersect two parallel lines, then alternate interior angles are equal. Is this system of axioms consistent ? Justify your answer.

The area of two sectors of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement trus ? Why ?

The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal ? Why ?