Medians and Altitudes

MEDIANS OF A TRIANGLE

 The line segment joining a vertex of a triangle to the mid point of its

opposite side is called a median of the triangle.

 A triangle has 3 medians

A

A

B

B

C

C

D

D

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ALTITUDES OF A TRIANGLE

 The perpendicular line segment from a vertex of a triangle to its opposite

side is called an altitude of the triangle.

 A triangle has 3 altitudes.

 Here the line segment AL is an altitude of the triangle.
A

B

C

L

ANGLE SUM PROPERTY OF A TRIANGLE

 The total measure of the three angles of a triangle is 180°.

 Angle sum property of a triangle states that, in a triangle ABC,

∠A + ∠B + ∠C= 180

A

B

C

EXAMPLE PROBLEM

 Find the measure of the missing angle in the given triangle ABC.

A

B
C

46

55

x

Solution:

 Let ∠A= x

 We know that,

The sum of the three angles of a triangle is 180°

∠A + ∠B + ∠C = 180°

x + 46° + 55° = 180°

x + 101° = 180°

x = 180° - 101°

x = 79°

​TRIANGLES

ASSIGNMENT

 Draw rough sketches of altitudes from A to BC for the following triangles

(i) Acute angled triangle

(ii) Obtuse angled triangle

(iii) Right angled triangle

 One of the angles of a triangle is 70º and the other two angles are equal.

Find the measure of each of the equal angles.

RECOMMENDED READINGS

 NCERT Textbook (7thStandard).

 Government Of Tamil Nadu Textbook (7thStandard).

 Government Of Tamil Nadu Textbook (8thStandard).

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