Exercises on the geometry and measurement of plane figures, being solutions of the theorems, problems and questions in 'Wormell's Modern geometry'.Thomas Murby, 1883 - 192 páginas |
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Página 12
... proved that the straight line which joins A with the middle point of B C is perpendicular to B C ; and in Example 8 it is proved that only one perpendicular can be drawn from A to B C. Hence the perpen- dicular from A to B C is also the ...
... proved that the straight line which joins A with the middle point of B C is perpendicular to B C ; and in Example 8 it is proved that only one perpendicular can be drawn from A to B C. Hence the perpen- dicular from A to B C is also the ...
Página 15
... prove that A M the half of AB + AC . B Continue A M to D and make M D = join D C. In the triangles A M B , D M C , M A M A , and CM = BM , A M = D M , and △ AMB = 4 DM C. Therefore the triangles are equal in all respects , and A B ...
... prove that A M the half of AB + AC . B Continue A M to D and make M D = join D C. In the triangles A M B , D M C , M A M A , and CM = BM , A M = D M , and △ AMB = 4 DM C. Therefore the triangles are equal in all respects , and A B ...
Página 18
... and B , on opposite sides of a line E F , are joined with a point C in EF . Prove that the dif- ference between A C and BC is greatest when the angles A CE , BCE are equal . A Let B be nearer to the line EF than 18 Theorems and Problems .
... and B , on opposite sides of a line E F , are joined with a point C in EF . Prove that the dif- ference between A C and BC is greatest when the angles A CE , BCE are equal . A Let B be nearer to the line EF than 18 Theorems and Problems .
Página 22
... 27. In any triangle , A B C , two lines , A D , A E , are drawn to BC , making △ BAD = △ C and LCAE = L. B. Prove that AED is an iso- sceles triangle In A ABD the exterior . ADC LABC + BAD 22 Theorems and Problems .
... 27. In any triangle , A B C , two lines , A D , A E , are drawn to BC , making △ BAD = △ C and LCAE = L. B. Prove that AED is an iso- sceles triangle In A ABD the exterior . ADC LABC + BAD 22 Theorems and Problems .
Página 24
... prove that when this middle line is greater than half the base the vertical angle is acute ; when the middle line is equal to half the base the angle is a right angle ; and when the middle line is less than half the base the vertical ...
... prove that when this middle line is greater than half the base the vertical angle is acute ; when the middle line is equal to half the base the angle is a right angle ; and when the middle line is less than half the base the vertical ...
Términos y frases comunes
A B and C D ABCD adjacent angles bisect the angle centre chord circum circumference common tangents Consequently Construct a triangle DAB+ Decagon describe a circle diagonals diameter equal to half equilateral triangle Find the area given angle given circle given radius given side given straight line gonals greater Hence hypothenuse inscribed circle isosceles triangle joining the middle LADC line joining line parallel middle line middle point opposite angles parallel to A B parallelogram pendicular pentagon perimeter perpendicular bisector perpendicular to A B point of intersection polygon quadrilateral R₁ radii radius a circle rectangle regular polygon required circle respectively equal rhombus right angle right-angled triangle square tangent touch a given triangle A B D triangle required vertex
Pasajes populares
Página 91 - 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.
Página 98 - 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.
Página 53 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Página 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.
Página 78 - To construct a circle which shall pass through two given points and touch a given straight line.
Página 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.
Página 159 - 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.
Página 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.
Página 30 - Any line drawn through the point of intersection of the diagonals of a parallelogram divides it into two equal quadrilaterals.
Página 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.