## Exercises on the geometry and measurement of plane figures, being solutions of the theorems, problems and questions in 'Wormell's Modern geometry'. |

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### Common terms and phrases

A B C D ABCD acres base centre chord circumference Consequently Construct a triangle contained Continue describe describe a circle diagonals diameter difference distance divided draw equal equal to half Example extremities figure formed four given angle given circle given point given radius given side given straight line greater half height Hence inscribed circle intersect isosceles triangle less Let A B C line joining lines drawn locus meet middle line middle point parallel parallelogram pass pentagon perimeter perpendicular point of intersection polygon problem produced Prove quadrilateral radii rect rectangle right angle sides Similarly square Take triangle triangle required twice vertex vertical yards

### Popular passages

Page 93 - If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the parts.

Page 100 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.

Page 54 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.

Page 40 - Thus, of all straight lines drawn from a given point to a given straight line, that which is perpendicular to the given line is a minimum.

Page 80 - To construct a circle which shall pass through two given points and touch a given straight line.

Page 90 - Two triangles are equal when they have two sides and the included angle of the one, respectively equal to two sides and the included angle of the other.

Page 161 - A field in the form of a right-angled triangle is to be divided between two persons, by a fence made from the right angle meeting the hypothenuse perpendicularly, at the distance of 880 links from one end ; required the area of each person's share, the length of the division-fence being 660 links. Ans. 2a. 3r.

Page 9 - If from any point within a triangle, two straight lines be drawn to the extremities of either side, their sum will be less than Hie sum of the two other sides of the triangle.

Page 30 - Any line drawn through the point of intersection of the diagonals of a parallelogram divides it into two equal quadrilaterals.

Page 46 - Ft, and to Dd. 23. The common intersection of the three lines divides each into two parts, one of which is double of the other, and this point is the vertex of three triangles which have lines drawn from it to the bisection of the bases. Apply Euc. n. 12, 13. 24. Apply Theorem 3, p.