The document defines and discusses the concept of altitudes in triangles. It defines an altitude as a segment drawn from a vertex perpendicular to the opposite side. It discusses that every triangle has three altitudes, one from each vertex, and that the three altitudes intersect at a single point called the orthocenter. The location of the orthocenter depends on whether the triangle is acute, right, or obtuse.

1. Altitude of triangle
Seema Kulkarni

2.  Subject – Mathematics
 Unit – Properties of triangle
 Subunit – Altitude of triangle
 Standard – 7th

3.  Properties of triangle
 Altitude of triangle
 Concept and definition of Altitude of triangle
 Concept of altitudes of triangle
 Altitudes in case of types of triangles based on angle (acute,
right, obtuse)
 Altitudes in case of types of triangles based on side (equilateral,
isosceles, scalene)
 Altitudes of triangle are concurrent

4.  In this figure,
M is the
midpoint of the
segment AB
A M B

5. Line l, line m,
line n are
bisectors of
seg AB A
l m
M
n
B
Line m is
perpendicular
bisector of seg
AB.

6. In figure, A, B, C are
the three vertices and
seg AB, seg AC and
seg BC are the three
sides of ABC
A
B C

7. In ABC, the seg AP
has been drawn
through the vertex A
perpendicular to side
BC.
A
Seg AP is called an B P C
Altitude..

8.  In DEF, the seg DM
has been drawn
through the vertex D
perpendicular to side
EF.
 Seg DM is called as an
____________.
D
E M F
Check the Answer

9.  In DEF, the seg DM
has been drawn
through the vertex D
perpendicular to side
EF.
D
Seg DM is called as an E M F
Altitude.

10.  In PQR, Altitude PS is
drawn from vertex P
and perpendicular to
opposite side QR.
P
Q S R

11. X
Y M Z
 In XYZ, Altitude XM
is drawn from
vertex and
perpendicular to
opposite side YZ.
Check the Answer

12.  In XYZ, Altitude XM
is drawn from
vertex X and
perpendicular to
opposite side YZ.
X
Y M Z

13.  In PQR, Altitude PS is
drawn from vertex P
and perpendicular
to opposite side
QR.
P
Q S R

14. X
Y M Z
 In XYZ, Altitude XM
is drawn from
vertex X and
perpendicular to
opposite side .
Check the Answer

15.  In XYZ, Altitude XM
is drawn from
vertex X and
perpendicular to
opposite side YZ.
X
Y M Z

16. Altitude - The line segment drawn from the vertex and
perpendicular to opposite side is an altitude of triangle.
Three altitudes can be drawn in any type of triangle.
 Altitudes of triangle are concurrent
 Intersection point of altitudes is called Orthocenter.
Position of Orthocenter –
 In acute angled triangle – inside the triangle region
 In right angled triangle – on the vertex where right angle is
formed
 In obtuse angled triangle – outside the region of triangle

17. Congratulations for
correct answers.
Thank You!!!