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8. In an isosceles triangle PQR, PQ = PR, the bisector of ∠P meets at S. P

Answer the following.
(a) Is DPQS ≅ DPRS? Give reasons.
Q S R
(b) Is S the mid-point of QR?
X
(c) Find ∠PSQ.
9. In the adjoining figure, XL ⊥ LM, YM ⊥ LM and XL = YM. L Z M
Prove that DZLX ≅ DZMY. Give reasons.

Is ZL = ZM? Why? Y
10. The roof of a building is 6 m high. A rope is tied from the roof to a peg on the ground 8 m away
from the wall. What is the shortest length of the rope?
11. Mamta walks 15 m East and 8 m South to reach the opposite corner of a rectangular field. Neeraj
walked from the same point diagonally to the opposite corner. What is the distance covered by
Neeraj?
COMPETENCY BASED QUESTION
12. A ladder 26 m long reaches a windows which is 10 m above the ground on the one side of the road.
Keeping its foot at the same point and turns the ladder to other side of the street to reach a window
at a height of 24 m. find the width of the street.
13. Draw an equilateral triangle of side 8 cm, an isosceles triangle of base 4 cm, and equal sides 6 cm
each and a scalene triangle of sides 4 cm, 5 cm, and 6 cm. Now draw a median and an altitude in
each triangle from the top vertex, measure and tabulate the lengths of all the medians and altitudes
of respective triangles. What can you conclude from this activity?

14. Nisha planted two neem seeds on his ninth birthday on the banks of the river flowing between
these plants and they both started growing into plants soon. After 25 years, when Nisha visited
that place, she saw two big neem trees. The two trees were 10 m and 7 m standing upright on CASE STUDY
the ground. The distance between their roots is 4 m apart.
(a) Which property can be used to find the distance between the tops of the trees?

(b) If the distance between their roots is 4 m apart, then what is the width of the river?
(c) What will be the distance between the tops of both trees?

Brain Sizzlers
A surveyor has to measure the length of a pond. He observes that two A B
trees are standing on opposite banks. He considered both the trees as 12 m C
points A and B, and to find the distance between these points makes a
right-angled triangle from his initial point as shown in the figure. Find the
length of the pond by finding the distance AB. 30 m 40 m

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