JIGAR PRO
... 3. The scale of a map is 1: 10 000. On the map, the area representing a plot of land is 3cm 2. Find the area of the field in m 2. 4. My lounge door is 800mm wide and a picture of the door is 20 mm wide. Find the ratio of the area of the picture of the door to the area of the actual door. 5. The side ...
... 3. The scale of a map is 1: 10 000. On the map, the area representing a plot of land is 3cm 2. Find the area of the field in m 2. 4. My lounge door is 800mm wide and a picture of the door is 20 mm wide. Find the ratio of the area of the picture of the door to the area of the actual door. 5. The side ...
Identifying Congruent Figures
... two angles of another triangle, then the third angles are also congruent. If A D and B E, then C F. ...
... two angles of another triangle, then the third angles are also congruent. If A D and B E, then C F. ...
Situation 43: Can You Circumscribe a Circle about this Polygon?
... through the points EFG (in general, through the 3 points that occur at the polygon’s interior angles that are not greater than 180 degrees – this is possible because a concave quadrilateral will have exactly one interior angle greater than 180 degrees, in this case it’s angle EHG). Suppose point H l ...
... through the points EFG (in general, through the 3 points that occur at the polygon’s interior angles that are not greater than 180 degrees – this is possible because a concave quadrilateral will have exactly one interior angle greater than 180 degrees, in this case it’s angle EHG). Suppose point H l ...
Taxicab Triangle Incircles and Circumcircles
... Definition 2.1 A taxicab angle is positively inscribed if a line of slope 1 through its vertex remains outside the angle. Definition 2.2 A taxicab angle is negatively inscribed if a line of slope -1 through its vertex remains outside the angle. Definition 2.3 A taxicab angle is inscribed if it is po ...
... Definition 2.1 A taxicab angle is positively inscribed if a line of slope 1 through its vertex remains outside the angle. Definition 2.2 A taxicab angle is negatively inscribed if a line of slope -1 through its vertex remains outside the angle. Definition 2.3 A taxicab angle is inscribed if it is po ...
Further Concepts in Geometry
... 1 and the given angle are alternate exterior angles and are congruent. So m1 75. 5 and the given angle are vertical angles. Because vertical angles are congruent, they have the same measure. So, m5 75. Similarly, 1 4 and m1 m4 75. There are several sets of linear pairs, includin ...
... 1 and the given angle are alternate exterior angles and are congruent. So m1 75. 5 and the given angle are vertical angles. Because vertical angles are congruent, they have the same measure. So, m5 75. Similarly, 1 4 and m1 m4 75. There are several sets of linear pairs, includin ...
History of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- ""earth"", -metron ""measurement"") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic).Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See Areas of mathematics and Algebraic geometry.)