TRIANGLES
Frequently Asked Questions
A triangle is a polygon with three sides, three vertices, and three angles.
Equilateral (all sides equal), Isosceles (two sides equal), Scalene (all sides different).
Acute (all angles < 90°), Right (one angle = 90°), Obtuse (one angle > 90°).
The sum of all interior angles of a triangle is always 180 degrees.
The exterior angle of a triangle equals the sum of the two opposite interior angles.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Triangles with equal corresponding sides and angles are congruent and can be superimposed on each other.
\(\text{SSS (Side-Side-Side),}\\ \text{SAS (Side-Angle-Side),}\\ \text{ASA (Angle-Side-Angle),}\\ \text{AAS (Angle-Angle-Side),}\\\small\text{RHS (Right angle-Hypotenuse-Side).}\)
Triangles with all three sides equal are congruent.
If two sides and the included angle are equal, the triangles are congruent.
If two angles and the included side are equal, the triangles are congruent.
For right triangles, if the hypotenuse and one side are equal, the triangles are congruent.
Area = (1/2) × base × height
By adding the lengths of all three sides. Perimeter = a + b + c
A line segment drawn from a vertex to the midpoint of the opposite side.
A perpendicular segment from a vertex to the opposite side (or its extension).
The point where all three altitudes of a triangle meet.
The point of intersection of the medians; also the triangle’s center of mass.
The point where the perpendicular bisectors of the triangle’s sides meet; it's the center of the circumcircle.
The point where the angle bisectors meet; it’s the center of the incircle.
Example: Acute scalene triangle, Right isosceles triangle, etc.
Proving two triangles in a geometric figure are equal for construction or calculation.
Angles opposite equal sides are also equal.
\(\angle A + \angle B + \angle C = 180^\circ\)
Triangles are used in construction for stability (trusses, roof supports) and navigation (triangulation).
Use any congruence criteria (SSS, SAS, ASA, AAS, RHS) with the given measurements.
Congruent triangles can be mapped onto each other using rigid motions (translation, rotation, reflection).
Engineering bridges, surveying equipment, architecture frames.
Because its sides support each other, making structures stable and rigid.
Look for side and angle markings, right angles, and parallel lines in diagrams.
Use coordinate geometry: \[A = \frac{1}{2} \Bigl[ x_1(y_2 - y_3)\\ + x_2(y_3 - y_1)\\ + x_3(y_1 - y_2) \Bigr]\]
No. Congruence requires matching sides and angles, not just area.
Area of triangle, angles in triangles, triangle calculator, properties of triangle class 9.
By solving NCERT exercises, extra questions, and drawing diagrams.
Read the problem carefully, note all given values, and draw or label the triangle.
Look for a 90° angle box or clues like “perpendicular.”
The base-height relationship for every triangle.
Triangles form the basis of sine, cosine, and tangent calculations.
Proving congruence, calculating area/perimeter, applying angle/side properties, giving real-life examples.
"Triangle ABC has sides 5 cm, 6 cm, 7 cm. Find the perimeter and area."
They help show congruence and symmetry, and are used in coordinate proofs.
The symbol for congruence is \(\cong\).
It forms a basis for proofs, constructions, and advanced mathematical concepts.
Equilateral triangle \(60^\circ, 60^\circ, 60^\circ \).
To check if three rods can make a triangle before construction.
Triangulation, which helps in finding exact positions using angles and distances.
Triangles are building blocks for rendering 3D shapes and textures.
(A) 180°, (B) 90°, (C) 360°, (D) 270°. Answer: (A) 180°
A triangle with all sides of different lengths and all angles different.
The angle sum property: add known angles and subtract from 180°.
