The foot of a ladder is 6 m away from its wall and its top reaches a
window 8 m above the ground, (a) Find the length of the ladder. (b) If
the ladder is shifted in such a way that its foot is 8 m away from the
wall, to what height does its top reach?
Two poles of 10 m and 15 m stand upright on a plane ground. If the
distance between the tops is 13 m, find the distance between their
feet.
State which of the following pairs of triangles are congruent. If yes,
write them in symbolic form (you may draw a rough figure).
(a) ∆ PQR : PQ = 3.5 cm, QR = 4.0 cm, ∠ Q = 60°
∆ STU : ST = 3.5 cm, TU = 4 cm, ∠ T = 60°
(b) ∆ABC : AB = 4.8 cm, ∠ A = 90°, AC = 6.8 cm
∆XYZ : YZ = 6.8 cm, ∠ X = 90° , ZX = 4.8 cm
If ∆PQR and ∆SQR are both isosceles triangle on a common base
QR such that P and S lie on the same side of QR. Are triangles PSQ
and PSR congruent? Which condition do you use?
Triangles DEF and LMN are both isosceles with DE = DF and
LM = LN, respectively. If DE = LM and EF = MN, then, are the two
triangles congruent? Which condition do you use?
If ∠ E = 40°, what is the measure of ∠ N?
The lengths of two sides of an isosceles triangle are 9 cm and 20 cm.
What is the perimeter of the triangle? Give reason.
Height of a pole is 8 m. Find the length of rope tied with its top from
a point on the ground at a distance of 6 m from its bottom.
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