In Δ PQR, D is the mid-point of \overline{QR}.
\overline{PM} is_.
Q1) In ∆ PQR, D is the mid-point of QR .
PM is _____________.
PD is _____________.
Is QM = MR?
Draw rough sketches for the following:
In ΔABC, BE is a median.
In ΔXYZ, YL is an altitude in the exterior of the triangle.
In ΔPQR, PQ and PR are altitudes of the triangle.
Q2) Draw rough sketches for the following:
(a) In ∆ABC, BE is a median.
(b) In ∆PQR, PQ and PR are altitudes of the triangle.
(c) In ∆XYZ, YL is an altitude in the exterior of the triangle.
Q3) Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.
Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.
Find the value of the unknown exterior angle x in the following diagram:
Q1) Find the value of the unknown exterior angle x in the following diagrams:
Q2) Find the value of the unknown interior angle x in the following figures:
(i}
(ii)
(iii)
(iv)
(v)
(vi)
Find the value of the unknown Interior angle x in the following figures:
Q1) Find the value of the unknown x in the following diagrams:
Find the value of the unknown x in the following diagrams:
Find the values of the unknowns x and y in the following diagrams:
Q2) Find the values of the unknowns x and y in the following diagrams:
6 cm, 3 cm, 2 cm
Is it possible to have a triangle with the following sides?
3 cm, 6 cm, 7 cm
Q1) Is it possible to have a triangle with the following sides?
(i) 2 cm, 3 cm, 5 cm
(ii) 3 cm, 6 cm, 7 cm
(iii) 6 cm, 3 cm, 2 cm
2 cm, 3 cm, 5 cm
Q2) Take any point O in the interior of a triangle PQR. Is
(i) OP + OQ > PQ?
(ii) OQ + OR > QR?
(iii) OR + OP > RP?
Take any point O in the interior of a triangle PQR. Is OP + OQ > PQ?
Take any point O in the interior of a triangle PQR. Is OR + OP > RP?
Take any point O in the interior of a triangle PQR. Is OQ + OR > QR?
AM is a median of a triangle ABC.
Is AB + BC + CA > 2 AM?
(Consider the sides of triangles ΔABM and ΔAMC.)
Q3) AM is a median of a triangle ABC. Is AB + BC + CA > 2 AM?
(Consider the sides of triangles ∆ABM and ∆AMC.)
Q4) ABCD is a quadrilateral. Is AB + BC + CD + DA > AC + BD?
ABCD is a quadrilateral.
Is AB + BC + CD + DA > AC + BD?
Q5) ABCD is quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD)?
ABCD is quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD)
Q6) The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?
The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?
Q1) PQR is a triangle, right-angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
PQR is a triangle, right-angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
Q2) ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC.
ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC.
Q3) A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
Which of the following can be the sides of a right triangle?
2 cm, 2 cm, 5 cm.
2.5 cm, 6.5 cm, 6 cm.
1.5 cm, 2cm, 2.5 cm.
In the case of right-angled triangles, identify the right angles.
Q4) Which of the following can be the sides of a right triangle?
(i) 2.5 cm,6.5 cm, 6 cm.
(ii) 2 cm, 2 cm, 5 cm.
(iii) 1.5 cm, 2cm, 2.5 cm.
A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.
Q5) A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.
Angles Q and R of a ΔPQR are 25° and 65° .
Write which of the following is true:
PQ2 + RP2 = QR2
Q6) Angles Q and R of a ∆PQR are 25\degree\ and\ 65\degree Write which of the following is true:
(i) PQ^2+QR^2\ =\ RP^2
(ii) PQ^2\ +\ RP^2\ =\ QR^2
(iii) RP^2\ +\ QR^2\ =\ PQ^2
Q7) Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.
Q8) The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.
The diagonals of a rhombus measure 16 cm and 30 cm. Find its Perimeter.
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