No. 33.
672
GEOMETRICAL DRAWING.
CLASS IV.
1. Define straight line, scalene triangle, trapezium, sector, tangent.
2. If you are given the length of three straight lines can you always construct a triangle with them? Give reasons for your answer.
3. Show how to construct a rhombus having given one side and the diagonals.
4. Divide a straight line 3 inches long into 4 equal parts and at each point erect a perpendicular 3 inches in length.
5. Divide a right angle into 8 equal parts.
No. 34.
GEOMETRY.
CLASSES I A and B.
5 Questions only to be answered. IA ought to attempt Question 6.
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 these sides equal, then the angles 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.
Prove the proposition.
If the straight line which bisects the external angle of a triangle is parallel to the opposite side shew that the triangle is isosceles.
3. At a given point in a straight Bae make an angle equal to a given angle.
Construct a triangle from the following data:—
6.5 cm b + c = 10 cm
B=60°
4. Prove that the area of a triangle is equal to one half the base multiplied by the altitude.
ABC is any triangle whose base BC is bisected at X. If is any point in the median AX, show that the triangle ABY-triangle ACY in area.
5. A ladder 50 ft. long is placed so as to reach a window 48 ft. high; and on moving the ladder over to the other side of the street it reaches a point 14 ft. high. Find the breadth of the street.
6. The tangent at any point of a circle is perpendicular to the radius at the point of contact.
From a given point as centre describe a circle to touch a given circle. How many solutions will there be?