SUMMARY / RELATED TOPICS

In geometry, a line segment is a part of a line, bounded by two distinct end points, contains every point on the line between its endpoints. A closed line segment includes both endpoints. Examples of line segments include the sides of a square. More when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge if they are adjacent vertices, or otherwise a diagonal; when the end points both lie on a curve such as a circle, a line segment is called a chord. If V is a vector space over R or C, L is a subset of V L is a line segment if L can be parameterized as L = for some vectors u, v ∈ V, in which case the vectors u and u + v are called the end points of L. Sometimes one needs to distinguish between "open" and "closed" line segments. One defines a closed line segment as above, an open line segment as a subset L that can be parametrized as L = for some vectors u, v ∈ V. Equivalently, a line segment is the convex hull of two points. Thus, the line segment can be expressed as a convex combination of the segment's two end points.

In geometry, it is sometimes defined that a point B is between two other points A and C, if the distance AB added to the distance BC is equal to the distance AC. Thus in R 2 the line segment with endpoints A = and C = is the following collection of points:. A line segment is a non-empty set. If V is a topological vector space a closed line segment is a closed set in V. However, an open line segment is an open set in V if and only if V is one-dimensional. More than above, the concept of a line segment can be defined in an ordered geometry. A pair of line segments can be any one of the following: intersecting, skew, or none of these; the last possibility is a way that line segments differ from lines: if two nonparallel lines are in the same Euclidean plane they must cross each other, but that need not be true of segments. In an axiomatic treatment of geometry, the notion of betweenness is either assumed to satisfy a certain number of axioms, or else be defined in terms of an isometry of a line.

Segments play an important role in other theories. For example, a set is convex if the segment that joins any two points of the set is contained in the set; this is important because it transforms some of the analysis of convex sets to the analysis of a line segment. The Segment Addition Postulate can be used to add congruent segment or segments with equal lengths and substitute other segments into another statement to make segments congruent. A line segment can be viewed as a degenerate case of an ellipse in which the semiminor axis goes to zero, the foci go to the endpoints, the eccentricity goes to one. A standard definition of an ellipse is the set of points for which the sum of a point's distances to two foci is a constant. A complete orbit of this ellipse traverses the line segment twice; as a degenerate orbit this is a radial elliptic trajectory. In addition to appearing as the edges and diagonals of polygons and polyhedra, line segments appear in numerous other locations relative to other geometric shapes.

Some frequently considered segments in a triangle include the three altitudes, the three medians, the perpendicular bisectors of the sides, the internal angle bisectors. In each case there are various equalities relating these segment lengths to others as well as various inequalities. Other segment

Our Lady of Fatima Academy is a private Roman Catholic school run by the Religious of the Virgin Mary in Davao City. It started in 1949 as Immaculate Conception College- Piapi School. In 1949, the Immaculate Conception College, Davao City, opened a free school in the slums of Piapi in this city through the initiative of the ICC Directress, Mother Maria Alberta Alviar, RVM; the old San Guillermo chapel served as classroom both for the kindergarten and grade one pupils with Mrs. Candida Josue and Miss Pancito as the first teachers; the following year an annex room was put up to accommodate the grade two and grade three classes with Mrs. Leonida Salas as additional teacher. In 1952, a complete primary course was offered. With the increasing enrollment, the need for a bigger space and rooms was seen into by Rev. Father Gaudiose Gagno, PME, the parish priest of Fatima Parish, he acquired a bigger place for both the Church and the School at the corner of Fatima and Aurora Streets. Due to limited space, some classes were held at nearby houses of a benefactor.

Teachers and school needs were provided by the Immaculate Conception College until such time when OLFA could stand on its own. With the help of ICC, OLFA parents and teachers worked for the improvement of the school. In 1954, the ICC- Piapi School was formally Changed to Our Lady of Fatima Academy. Four years the grade school was granted the government recognition. A new building was constructed in 1960 to accommodate the increase in enrollment; the complete secondary course was recognized in 1962. Enrollment continued to increase and so a new building was constructed in 1987; the wooden dilapidated building was knocked down for another construction of a concrete grade school building and made ready in 1994. In 1998, OLFA has produced one Most Outstanding Graduate in Davao City besting fifty- one other Valedictorians in the city and suburbs. On December 20, 1998, the school joined the start of a year -long Golden Jubilee of the Year of God the Father celebration and on January 1999, OLFA commemorated its Golden Jubilee of Foundation.

Enrollment continued to increase so on March 27, 2002, the laying of the cornerstone of a four-storey building took place. The actual construction started on April 2 of the same year; the improvement continued with the renovation of offices. The year marked the participation of OLFA in the Educational Service Contracting scheme of the government. In 2005, the RVM community headed by S. Ma. Lydia C. Daga, RVM, initiated the purchase of a 234 square meter lot fronting Fatima Church for the construction of a four-storey building to accommodate the continuing increase of enrollees every year; the groundbreaking was done on March 20, 2006. The building was blessed on December 30, 2006 and became the second home of the kindergarten and the intermediate classes since 2007. To continue the improvement of the school facilities needed to provide quality instruction, the administration had the faculty and audio-visual rooms renovated in the summer of 2007; as the buildings became concrete, the need to improve instruction and facilities were priorities hand-in-hand with the building preparations.

Improvement of facilities goes on to upgrade services to the school community. Computer lessons were incorporated into the curriculum, and therefore construction of computer laboratories, Speech laboratory and upgraded science laboratory, Home Economics and Industrial Arts rooms were seen into. In addition to that, right during S. Ma. Bernadette G. Suico, RVM's last reigning for Principal and Directress in 2013, all rooms are air-conditioned for improving enough ventilation. OLFA is up into the upgrading of the whole school, it has applied for accreditation with the Philippine Accrediting Association of Schools and Universities. July 24-25 the PAASCU Accreditors will be visiting the school Venerable Ignacia del Espíritu Santo known as Mother Ignacia was a Filipino Religious Sister of the Roman Catholic Church. Known for her acts of piety and religious poverty, founded the Congregation of the Sisters of the Religious of the Virgin Mary, the first native Filipino female congregation with approved pontifical status in what is now the Republic of the Philippines.

Mother Ignacia del Espiritu Santo was declared Venerable by Pope Benedict XVI in 2007. The school seal is derived from the seal of Religious of the Virgin Mary. Encircled by rays which represent the far-reaching zeal and charity, the central device is the A and M monogram representing the words Auspice Maria. Surrounding the Auspice Maria are twelve stars which stand for the twelve God-given prerogatives of Mary, the Mother of God and Mother of the Church through which people receive of her special and maternal blessings. Rays emanate from the starry monogram in seven groups, representing the light and wisdom from God through Jesus Christ, the light of the World, through Mary and reflect the Congregation's motto, "To Jesus through Mary". Under the monogram is an open book bearing the Latin inscription, Initium sapientiae Timor Domini, beginning of Proverbs 9:10: "The fear of the LORD is the beginning of wisdom", it expresses the filial fear, a disposition of profound reverence and love for God, the Source of all wisdom and life.

The sampaguita beneath the book symbolizes the purity of heart of Mary and Mother Ignacia and the Filipino origin of the school. The school name is written on the upper part of the seal and written below is Davao City, the locale of the school and 1949, the year the school was established; this logo is the same as every RVM Schools UIC, St. Mary's it just chan

Chris Tang Ping-keung, PDSM is the current Commissioner of Police of the Hong Kong Police Force since 19 November 2019. Taiwan News has described Tang as being considered a hardliner regarding the 2019 Hong Kong protests. Chris Tang has received training and education from various institutions, including the Federal Bureau of Investigation National Academy in Quantico, Royal College of Defence Studies, in London, the China Executive Leadership Academy in Pudong, Shanghai, he holds a Bachelor's degree in Social Science, a Master's degree in Business Administration and a Master's degree in International Security and Strategy. Tang was educated at the Chinese University of Hong Kong and received a Bachelor's degree in Social Science in 1987, he joined the Royal Hong Kong Police Force in the same year as an inspector. He spent many years working in the criminal investigation, international liaison and operational command, he was seconded to Interpol General Secretariat in Lyon as a specialised officer from 2006 to 2008, before he was promoted in the organisation as the head of Criminal Organisation and Violent Unit.

In 2015, Tang was appointed Assistant Commissioner of Police and discharged duties as regional commander of Hong Kong Island and Assistant Commissioner, Personnel. He was promoted to the rank of Senior Assistant Commissioner and appointed as Director of Operations before he became Deputy Commissioner of Police, he was awarded the Police Distinguished Service Medal in 2018. Tang was appointed the Commissioner of Police by the State Council of China in November 2019, succeeding Stephen Lo amid the widespread 2019 Hong Kong protests, at a time when police were under unrelenting criticism for excessive use of force, he was in charge of the police operation code-named Tiderider since the beginning of the protests. He has stated that the police are against having an independent inquiry into allegations of police brutality, a key demand from the protesters, claimed "fake news" was undermining the reputation of his police force. Following Tang's appointment as the Commissioner of Police in November 2019, the police changed its motto from "We serve with pride and care", used for more than 20 years, to "Serving Hong Kong with honour and loyalty."

According to the Taiwan News he "is known as a hardliner in the conflict with the pro-democracy protesters." He has said the violence perpetrated by activists is "very close to terrorism."