Revision Guide: A Tale of Three Intersecting Lines

A triangle is a closed shape with three vertices and three sides linking them.

Triangles are named based on their vertices, e.g., ΔABC can be named as ABC.

Triangles can be equilateral, isosceles, and scalene based on side length equality.

All sides and angles are equal; each angle measures 60°.

The sum of interior angles in a triangle is always 180°.

Use a compass and ruler to ensure accurate triangle side lengths; utilize arcs.

The sum of any two sides of a triangle must be greater than the third side.

If side lengths meet the triangle inequality, a triangle can be constructed.

Lengths like 10, 15, 30 do not satisfy triangle inequality, hence can't form a triangle.

An altitude is a perpendicular segment from a vertex to the opposite side.

Has at least two equal sides and angles; symmetry about the axis through the apex.

All sides and angles are different; no equal sides or angles.

Classifications based on angle measures: acute (<90°), right (90°), obtuse (>90°).

A compass ensures accurate lengths while constructing triangles; reduces errors.

Intersection points of two circles help find triangle vertices accurately.

A line that divides a segment into two equal parts at right angles.

Construct ∆ABC with sides 4 cm, 5 cm, 6 cm using compass arcs for precision.

Triangles are used in architecture and engineering for support and stability.

Diagrams help visualize triangles; essential for clear understanding and solving problems.

Area = 1/2 × base × height; critical for solving many geometric problems.

Remember that the angle sum must equal 180°; check this for each triangle.