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THE TRIANGLE AND ITS PROPERTIES

Classification of Triangles Classification of Triangles Median of a Triangle
Based on Sides Based of Angles The line joining the midpoint of
Scalene Triangle Acute-angled Triangle a side of a triangle to its opposite
A triangle in which all sides A triangle that has all acute vertex. B
are unequal in lengths. angles (less than 90°).
D E
Equilateral Triangle Obtuse-angled Triangle
A triangle that has all its sides A triangle in which one angle is A F C
of equal lengths. obtuse (greater than 90°).
Altitude of a Triangle
Isosceles Triangle Right-angled Triangle A perpendicular line from the
A triangle that has two of its A triangle that has one right vertex of a triangle to its opposite
sides of equal lengths. angle. side.
Q Q
Altitude from
QS to PR
P S R S P R
Interior and Exterior angles Angle Sum Property
of a Triangle The sum of all three

B B angles of a triangle is
180°.
A C A C Triangle Inequality
Interior Exterior The sum of the lengths Congruence Criteria
angles angles of any two sides of a SSS Congruence
Exterior Angle Property triangle is always A P
greater than the third If AB = PQ, BC = QR,
The exterior angle of a triangle side. AC = RP, then DABC ≅ DPQR
is equal to the sum of the two B C Q R
interior opposite angles. SAS Congruence

If AB = PQ, BC = QR and A P
∠ABC = ∠PQR, then

Pythagoras Theorem DABC ≅ DPQR B C Q R
ASA Congruence
The square of the hypotenuse of a right- If ∠B = ∠Q, ∠C = ∠R and A P
angled triangle is equal to the sum of the BC = QR, then DABC ≅ DPQR
squares of the other two sides. leg a hypotenuse c AAS Congruence B C Q R
2
2
c = a + b 2 A P
If ∠A = ∠P, ∠B = ∠Q and
leg b AC = PR, then DABC ≅ DPQR
B C Q R
RHS Congruence
If ∠B = ∠Q = 90°, A P
BC = QR and
AC = PR, then
DABC ≅ DPQR B C Q R

191 The Triangle and Its Properties