Page 174 - Math_Genius_V1.0_C7_Flipbook

D:\Surender Prajapati\CBSE_ICSE_Book_New\CBSE\Grade-7\Math_Genius-7\Open_File\08_Chapter\08_Chapter
\ 15-Nov-2024 Surender Prajapati Proof-6 Reader’s Sign _______________________ Date __________

(b) In DABC,

Sides: AB = BC = 4 cm, AC = 7 cm (two sides are equal)
Vertices: A, B and C
Angles: ∠A, ∠B and ∠C (∠B is an obtuse angle)

So, DABC is an isosceles and obtuse-angled triangle.
(c) In DPQR,

Sides: PQ = QR = 6 cm, and PR (two sides are equal)
Vertices: P, Q and R
Angles: ∠P, ∠Q and ∠R and ∠Q is a right angle.

So, DPQR is an isosceles right-angled triangle.
(d) In DPQR,
Sides: PQ = 10 cm, QR = 6 cm and PR = 8 cm (all sides are unequal)

Vertices: P, Q and R
Angles: ∠P, ∠Q and ∠R and ∠R is a right-angled triangle.

So, DPQR is a scalene and right-angled triangle.
Medians and Altitudes of a Triangle

Median

activity
Take a paper sheet and draw a triangle ABC on it.
Cut out the triangle ABC from the sheet.
Consider any one of its sides, say BC and by paper folding locate the perpendicular bisector of side BC.
Unfold the triangle, the folded crease meets BC at D, that represents the midpoint of side BC.
Now, Join AD.
A A

B D C
B D C
The line segment AD, joining the mid-point of BC to its opposite vertex A is called a median of DABC.

Thus, a line segment joining a vertex and the midpoint of its A
opposite side is called a median of the triangle.
F E
Extend the above activity by considering other two sides AC
and AB of the triangle ABC to find more medians of the
triangle. B D C
In the adjoining figure in DABC, AD, BE, and CF are the
medians drawn from the vertex A, B, and C respectively, Think and Answer
to the respective opposite sides BC, AC, and AB. Does a median lie in the interior of a
Hence, a triangle has three medians. triangle entirely? If not, then give reason.

Mathematics-7 172