Worksheet 2
1. The lengths of the midlines of a triangle are given. How long are the sides? Which of the
triangles is a right triangle?
a) 6cm; 7cm; 12cm
b) 15cm; 36cm; 39cm
c) 3cm; 4cm; 7cm
2. In a right triangle the legs are 21cm and 72cm. Determine the length of the medians.
3. Compute the radius of the inscribed circle of the right triangle with the following legs:
65 cm and 72 cm.*
4. The lengths of the medians of an isosceles triangle are 90, 51, 51. What is the length of the
sides?
5. Calculate the length of the sides of an equilateral triangle inscribed in a circle of radius 10.
6. HW The side of a regular triangle is 2cm longer than the altitude. What is the perimeter of
the triangle?
7. The triangles ABC and PQR are congruent. What is the value of
∠ABC?
8. The triangles below are congruent. What is the perimeter of the triangle PQR?
9. ΔABC ≅ ΔPQR. Find the length of PM.
10. ΔAPQ ∼ ΔACB. If AQ = 2 cm, PC = 5 cm, QB = 13 cm and BC = 15 cm, then find the
length of AP rounded to the nearest decimal.
11. ΔABC is similar to ΔPQR. AB = 12 cm, BC = 13 cm and AC = 10 cm. If PQ = 5 cm, then
find the measures of QR and PR in cm.
12. In the figure, AB || DE. AC = 4 cm, CE = 6 cm and DB = 15 cm. Find BC.
13. D is a point on side BC of ΔABC such that ∠
, then what is the length of
?*
∠
. If
and
14. In a right triangle the altitude corresponding to the hypotenuse divides the hypotenuse into
a 8cm and a 18cm long part. Calculate the length of the sides.
15. *HW The hypotenuse of a right triangle is 39cm, one of the legs is 15cm long. Calculate
the perimeter, the area, the radius of inscribed and the circumscribed circles, the heights,
the lengths of the medians.
16. A right triangle ABC has the following legs: a = 4, b = 3. Find sine, cosine and tangent of
angle .
17. A leg a = 0.324, a hypotenuse c = 0.544. Find the second leg b and the angles  and .
18. HW Given: hypotenuse c = 13.65m and acute angle  = 54°17’.Find another acute angle
 and legs a and b.
19. In a right triangle,
. Sketch the triangle and evaluate
20. One of the angles of an isosceles triangle is
How long are the sides of the triangle? *
.
, the radius of the inscribed circle is .
21. Solve the right triangle shown below.
22. The length of one of the sides of a right triangle is
. The angle opposite this side is
. What is the length of the largest altitude of this triangle?
23. In a triangle
a)
,
units, the altitude from the side is
b)
. Solve the triangle. *
units (i.e.
) and
24. The length of the hypotenuse of a right triangle is units, and the length of the altitude
drawn to the hypotenuse is √ units. Solve the right triangle. *
25. Compute the radius of the circumscribed circle of the right triangle in which the lengths of
the perpendicular sides are 28 cm and 45 cm.