The Triangle and its Properties
PD is _____
Is QM = MR ?
2. Draw rough sketches for the following:
In A ABC, BE is a median.
In A PQR, PQ and PR are altitudes of the triangle.
In A XYZ, YL is an altitude in the exterior of the triangle.
3. Verify by drawing a diagram if the median and altitude of a isosceles triangle can be same.
4. Find the value of the unknown exterior angle x in the following diagrams:
5. Find the value of the unknown interior angle x in the following figures:
6. Find the value of unknown x in the following diagrams:
7. Find the values of the unknowns x and y in the following diagrams:
8. 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
9. Take any point 0 in the interior of a triangle PQR. Is:
(i) OP + OQ > PQ ?
(ii) OQ + OR > QR ?
(iii) OR + OP > RP ? Since sum of two sides is greater than third side.
10. AM is a median of a triangle ABC. Is AB + BC + CA > 2AM?
(Consider the sides of triangles Δ ABM and Δ AMC.)
11. ABCD is a quadrilateral. Is AB + BC + CD + DA > AC + BD?
12. ABCD is quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD)?
13. 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?
14. PQR is a triangle, right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
15. ABC is a triangle, right angled at C. If AB = 25 cm and AC = 7 cm, find BC.
16. 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.
17. Which of the following can be the sides of a right triangle?
(i) 5 cm, 6.5 cm, 6 cm
(ii) 2 cm, 2 cm, 5 cm
(iii) 1.5 cm, 2 cm, 2.5 cm
In the case of right angled triangles, identify the right angles.
18. 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.
19. Angles Q and R of a Δ PQR are 25° and 65°. Write which of the following is true:
(i) PQ2 + QR2 = RP2
(ii) PQ2 + RP2 = QR2
(iii) RP2 + QR2 = PQ2
20. Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.
21. The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.