Class 9 Maths • Chapter 07 • Comprehensive Guide
Triangles are the strongest shape in geometry. Every bridge, tower, and roof uses triangles because they don’t deform easily.
CBSE Insight: Many geometry questions reduce to triangle logic.
Two triangles are congruent if they are copies of each other and when superimposed, they cover each other exactly.
CPCT: Corresponding Parts of Congruent Triangles are equal.
Two triangles are congruent if two sides and the included angle of one are equal to the corresponding sides and angle of the other.
⚠ Common mistake: Angle must be between the two given sides.
Two triangles are congruent if two angles and the included side of one are equal to the corresponding parts of the other.
Two triangles are congruent if any two angles and a non-included side of one are equal to the corresponding parts of the other.
Two triangles are congruent if three sides of one triangle are equal to the corresponding three sides of the other.
For right-angled triangles, if the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other.
Click parts of the triangle to see the theorem!
Theorem: Angles opposite equal sides of an isosceles triangle are equal.
Can these sides form a triangle?
CBSE Tip: Write full theorem statements for theory marks.
1. In \( \Delta ABC \), if \( AB = AC \), then:
2. Which is NOT a criterion for congruence of triangles?
3. In a right triangle, the longest side is:
4. If two sides of a triangle are unequal, the angle opposite to the longer side is:
5. Can 3cm, 4cm, and 8cm form a triangle?