Exercises for Chapter I

1. Classify each of the following angles as acute, right, obtuse, or not possible in a triangle:

-30^o, 0^o, 90^o, 156^o, 180^o, 360^o.

2. Tell which of the following pairs of angles are possible in the same triangle and find the third angle in each such case:

    (a) 90^o, 90^o;       (b) 100^o, 85^o;       (c) 50^o, 60^o;      (d) 30^o, 140^o.

3. Find (i) the exact value and (ii) a two decimal approximation (See Preface) for v in each of the following triangles:

4. Of the following triples, first identify those which represent sides of a triangle. Of those, select the right triangles and identify them. Then pick out the 45^o, 45^o, 90^o triangles and the 30^o, 60^o, 90^o triangles:

(a)     (b) 2, 3, 11     (c) 5, 12, 13

(d) 8, 9, 11 (e) 3, 3, (f) 1, 2,

(g) 1, (h) (i) 7.11, 9.48, 11.85

5. Given that is similar to find x and y.

6. Which angle in is equal to angle A?

7 (a) Is a triangle with sides similar to one with sides

   (b) Is a triangle with sides 23.472, 41.144, 51.256 similar to one with side 55.1592, 96.6884, 110.2004?

8. Which of the following pairs of triangles are similar? Justify your answers.

9. Given: angles A and A' are equal.     (a) Find u and v in terms of r, a, and b.     (b) If a = 2.6 and b = 1.1 find r, u, and v to 3 decimal places.

10. Are any two 30^o, 60^o, 90^o triangles similar? Justify your answer.

11. Explain why a triangle whose sides are of length is a right triangle. (Of course, a > 0 and b > 0.)

12. Complete the following table for converting certain degree measures to radians or, when read properly, radians to degrees:

in degrees	0o	30o	45o			120o		150o	180o
in radians	0

13. Given that and that show that

14. Show that the quadrilateral ABCD is a parallelogram if and only if is similar to with

15. Prove that AEFG is a parallelogram, given that ABCD is a parallelogram, and

16. Use the methods depicted in Figure 9b and in Figure 9c in Section 4 to show how to construct the angles given below with 30^o, 60^o, 90^o and 45^o, 45^o, 90^o triangles.

     (a) 105^o;      (b) 15^o;       (c) 225^o;      (d) 135^o;       (e) 195^o.

17. Let in Let a, b, and c stand for the lengths of sides opposite and respectively. Find:

     (a) c when a = 5 and b = 12

     (b) b when a = 8 and c = 17

     (c) when and c = 8

     (d) when and c = 10.

18. Given a unit length, outline the construction with straightedge and compass of lengths of

     (a) 2/3                  (b)