Medians and Altitudes

TRIANGLES

(MEDIANS, ALTITUDES AND ANGLE SUM PROPERTY OF TRIANGLE)

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

||

||

||

||

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°

QUIZ TIME



LETS PLAY.....

​TRIANGLES

Multiple Choice

In ∆ PQR, D is the mid-point of QR .

PM is _________________.

PD is _________________

• PM - Altitude, PD - Median.

• PM - Median, PD - Altitude.

• PM - Not Altitude, PD - Median.

• PM - Altitude, PD - Not Median

Multiple Choice

Which triangle has the same altitude and median from the vertex A?

Multiple Choice

How many MEDIANS can a triangle have?

How many ALTITUDES can a triangle have?

• 3, 4

• 6, 3

• 4, 3

• 3, 3

Multiple Choice

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

• 80 degrees

• 45 degrees

• 70 degrees

• 90 degrees

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).

THANK YOU