Sessional_Paper_1907 — Page 1069

No. 35.

673

GEOMETRY.

CLASS II.

1. If two triangles have two sides of the one equal to two sides of the other each to each, and the angles included by those sides equal, then the triangles are equal in all respects. Prove this proposition.

Discuss the case where two triangles have two sides and an angle. not the included angle, equal.

2. If a straight line cuts two other straight lines so as to make the alternate angles equal, the two straight lines are parallel.

3. (1) Prove that the sum of the angles of any quadrilateral is equal to 4 right angles.

(2) How many sides have the regular polygons whose angles are (a) 108° (b) 156°.

4. Prove that the diagonals of a rhombus bisect one another at right angles.

5. In a triangle ABC the base angles at B & C are bisected by BO

A and CO respectively, show that BOC = 90° +

2

No. 36.

GEOMETRY.

CLASS III.

1. Define the following terms —

Plane, circle, perpendicular, median.

2. If two triangles have two sides of the one equal to two sides of the other, cach to each, and the angles included by those sides equal, then the triangles are equal in all respects.

Prove the proposition.

3. If two angles of a traingle are equal to one another then the sides which are opposite to the equal angles are equal to one another.

4. If ABCD is a rhombus and the diagonals cut one another at Ø, Prove:-

(1) Angle ABC-angle ADC.

(2) AC bisects each of angles BAD, BCJ),

(3) BO=OD.

(4) AOB, AOD are right angles.

5. The earth raakes a complete revolution about its axis in 24 hours. Through what angle will it turn in 3 hours 20 minutes, and how long will itt ake to turn through 130°?