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QUEEN'S COLLEGE, HONGKONG. ANNUAL EXAMINATION, 1896.
EUCLID.
Class I. A.
1. Classify the different kinds of triangles (a) according to their sides, and (b) according to their
angles.
2. Prove that-If two angles of a triangle be equal, the sides also which are opposite to the equal
angles are equal to one another.
What is the corollary to this proposition?
3. If a side of any triangle be produced the exterior angle is equal to the two interior and opposite
angles, and the three interior angles of every triangle are together equal to two right angles.
4. If the square described on one of the sides of a triangle be equal to the sum of the squares described on the other two sides, the angle contained by these two sides is a right angle. Enunciate the converse of this proposition.
5. To divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part. In what proposition in this construction first used in Euclid ?
6. To draw from a given point without the circumference a straight line which shall touch a given
circle.
7. The opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. 8. To inscribe a circle in a given triangle.
9. Two circles intersect: prove that the common chord is bisected at right angles by the straight line
joining their centres.
10. Prove that the bisectors of the angles at the base of an isosceles triangle cannot meet at right
angles.
Classes I. B & I. Ca.
1. Define a straight line, a circle, a plane, a parallelogram, a triangle, and classify the triangles
according to their sides.
2. Prove that-If two angles of a triangle be equal, the sides also which are opposite to the equal
angles shall be equal to one another.
What is the corollary to this proposition?
3. If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite
angles.
4. Parallelograms on equal bases and between the same parallels are equal to one another.
5. If the square described on one of the sides of a triangle be equal to the sum of the squares described on the other two sides, the angle contained by these two sides is a right angle.
6. To divide a given straight line into two parts, so that the rectangle contained by the whole line
and one part may be equal to the square on the other part.
7. To draw from a given point without the circumference a straight line which shall touch the given
circle.
8. The opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. 9. Two circles intersect: prove that the common chord is bisected by the straight line joining their
centres.
10. Prove that the bisectors of the angles at the base of an isosceles triangle cannot meet at right angles.
Classes I. Cb. & II. A.B.
1. Define a straight line, a scalene triangle, a plane, a circle, a rhombus.
2. Enunciate Proposition 4 of Book I.
3. Prove that—If two angles of a triangle be equal, the sides also which are opposite to the equal
angles are equal to one another.
What is the corollary to this proposition?
4. To draw a straight line perpendicular to a given straight line of unlimited length from a given
point without it.
Why must we say of unlimited length?
5. Any two sides of a triangle are together greater than the third side.
6. If a side of a triangle be produced the exterior angle is equal to the two interior and opposite
angles.
7. If a parallelogram and a triangle be on the same base and between the same parallels, the
parallelogram shall be double of the triangle.