TRIANGLES - True/False

The Basic Proportionality Theorem (Thales' theorem) states that if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides in the same ratio.

In a triangle, a line parallel to one side always intersects the other two sides externally.

The converse of the Basic Proportionality Theorem is valid, meaning if a line divides two sides of a triangle proportionally, it must be parallel to the third side.

Triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

Two triangles with two pairs of equal corresponding angles are always similar.

The SSS similarity criterion states that three sides of one triangle are proportional to three sides of another triangle implies similarity.

SAS similarity holds if two sides of one triangle are proportional to two sides of another and the included angles are equal.

All congruent triangles are similar.

The ratio of areas of two similar triangles equals the square of the ratio of their corresponding sides.

In right-angled triangles, the square of the hypotenuse equals the sum of squares of the other two sides.

The converse of Pythagoras theorem is false for right-angled triangles.

A line segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long.

Similar triangles always have equal areas.

If two triangles have all three angles equal, their sides must be equal in length.

In \(\mathrm{\Delta ABC}\) and \(\mathrm{\Delta DEF}\), if \(\mathrm{AB/DE = BC/EF}\) but angles at \(\mathrm{B}\) and \(\mathrm{E}\) differ, the triangles cannot be similar.

The Basic Proportionality Theorem applies only to equilateral triangles.

Pythagoras theorem applies to any triangle, not just right-angled ones.

Areas of similar triangles are proportional to the product of their corresponding sides.

A triangle with sides 3, 4, 5 cm satisfies Pythagoras theorem.

In similar triangles, corresponding altitudes are proportional to their sides.

The AAA similarity criterion requires all three angles to be equal.

If \(\mathrm{DE \parallel BC}\) in \(\mathrm{\Delta ABC}\), then \(\mathrm{\Delta ADE \sim \Delta ABC}\) by AAA similarity.

Two triangles with equal perimeters must be similar.

The ratio of areas of \(\mathrm{\Delta ABC}\) to \(\mathrm{\Delta DEF}\) is 4:9 if their similarity ratio is 3:2.

Pythagoras theorem can prove if a triangle is isosceles right-angled.