A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, C is denoted △ A B C. In Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane. In other words, there is only one plane that contains that triangle, every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; this article is about triangles in Euclidean geometry, in particular, the Euclidean plane, except where otherwise noted. Triangles can be classified according to the lengths of their sides: An equilateral triangle has all sides the same length. An equilateral triangle is a regular polygon with all angles measuring 60°. An isosceles triangle has two sides of equal length. An isosceles triangle has two angles of the same measure, namely the angles opposite to the two sides of the same length; some mathematicians define an isosceles triangle to have two equal sides, whereas others define an isosceles triangle as one with at least two equal sides.
The latter definition would make all equilateral triangles isosceles triangles. The 45–45–90 right triangle, which appears in the tetrakis square tiling, is isosceles. A scalene triangle has all its sides of different lengths. Equivalently, it has all angles of different measure. Hatch marks called tick marks, are used in diagrams of triangles and other geometric figures to identify sides of equal lengths. A side can be marked with a pattern of short line segments in the form of tally marks. In a triangle, the pattern is no more than 3 ticks. An equilateral triangle has the same pattern on all 3 sides, an isosceles triangle has the same pattern on just 2 sides, a scalene triangle has different patterns on all sides since no sides are equal. Patterns of 1, 2, or 3 concentric arcs inside the angles are used to indicate equal angles. An equilateral triangle has the same pattern on all 3 angles, an isosceles triangle has the same pattern on just 2 angles, a scalene triangle has different patterns on all angles since no angles are equal.
Triangles can be classified according to their internal angles, measured here in degrees. A right triangle has one of its interior angles measuring 90°; the side opposite to the right angle is the longest side of the triangle. The other two sides are called the catheti of the triangle. Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse. Special right triangles are right triangles with additional properties that make calculations involving them easier. One of the two most famous is the 3–4–5 right triangle, where 32 + 42 = 52. In this situation, 3, 4, 5 are a Pythagorean triple; the other one is an isosceles triangle. Triangles that do not have an angle measuring 90° are called oblique triangles. A triangle with all interior angles measuring less than 90° is an acute triangle or acute-angled triangle.
If c is the length of the longest side a2 + b2 > c2, where a and b are the lengths of the other sides. A triangle with one interior angle measuring more than 90° is an obtuse triangle or obtuse-angled triangle. If c is the length of the longest side a2 + b2 < c2, where a and b are the lengths of the other sides. A triangle with an interior angle of 180° is degenerate. A right degenerate triangle has collinear vertices. A triangle that has two angles with the same measure has two sides with the same length, therefore it is an isosceles triangle, it follows that in a triangle where all angles have the same measure, all three sides have the same length, such a triangle is therefore equilateral. Triangles are assumed to be two-dimensional plane figures. In rigorous treatments, a triangle is therefore called a 2-simplex. Elementary facts about triangles were presented by Euclid in books 1–4 of his Elements, around 300 BC; the sum of the measures of the interior angles of a triangle in Euclidean space is always 180 degrees.
This fact is equivalent to Euclid's parallel postulate. This allows determination of the measure of the third angle of any triangle given the measure of two angles. An exterior angle of a triangle is an angle, a linear pair to an interior angle; the measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it. The sum of the measures of the three exterior angles of any triangle is 360 degrees. Two triangles are said to be similar if every angle of one triangle has the same measure as the corresponding angle in the other triangle; the corresponding sides of similar triangles have lengths that are in the same proportion, this property is sufficient to establish similarity. Some basic theorems about similar triangles are: If and only if one pair of internal angles of two triangles have the sam
The 1930 Alabama Crimson Tide football team represented the University of Alabama in the 1930 college football season. It was the Crimson Tide's 37th 9th season as a member of the Southern Conference; the team was led by head coach Wallace Wade, in his eighth year, played their home games at Denny Stadium in Tuscaloosa, at Legion Field in Birmingham, at the Cramton Bowl in Montgomery, Alabama. They finished the season with a perfect record, as Southern Conference champions and as national champions after they defeated Washington State in the Rose Bowl. In April 1930, coach Wade announced his resignation effective at the end of the 1930 season, his last Alabama team might have been his best. For psychological effect, Wade started games with his second team, the backups never allowed a point; the first team defense only allowed the opposition to score 13 points over the course of the season en route to a 9–0 record. Only the Vanderbilt game was close, as the Commodores scored a late touchdown that cut Alabama's lead to five in their 12–7 loss.
Vanderbilt's touchdown and a touchdown scored by Tennessee accounted for all of the scoring by Alabama's opponents in 1930. Alabama received its third Rose Bowl invitation in six seasons, this time against the undefeated Cougars of Washington State. In the game, Wade started his second team. Once again, the second team did not allow any points and neither did the first team in their 24–0 victory; the win clinched the second perfect season in school history after 1925, the Crimson Tide claimed the 1930 national championship along with the Notre Dame Fighting Irish. Johnny Cain starred at fullback, in the days of iron man football handled linebacker, punting duties, he was inducted into the College Football Hall of Fame. Other players from the 1930 Alabama team included Fred Sington, who went on to play baseball for the Washington Senators and Frank Howard, who became famous as the long-time head coach at Clemson. Jennings B. Whitworth, who kicked a field goal in the Rose Bowl, was hired as Alabama's football coach a quarter-century later.
After eight seasons as Alabama's head coach, on April 1, 1930, Wallace Wade announced he would resign his position at the conclusion of the 1930 season to take the same position with Duke. At the time of his announcement, Wade did not give a reason for his departure other than that his contract was set to expire on September 1, 1931. Although never publicly stated by Wade himself and former players attributed his resignation to criticism he received during the 1927, 1928, 1929 seasons, as well as his desire to return to a private university. Wallace Wade completed his Alabama tenure with a 61–13–3 record, four conference titles, three national championships, he coached several star players as well. Wade followed up his success at Alabama with a longer and as successful run at Duke, was inducted into the College Football Hall of Fame. Source: Rolltide.com: 1930 Alabama football schedule Alabama opened the season with its only scheduled non-conference game against Howard College at Denny Stadium.
Before an estimated crowd of 6,000 fans, Alabama shutout Howard 43–0. After a scoreless first quarter, the Crimson Tide scored 34 second-quarter points. Touchdowns were scored on runs by Johnny Cain, John Suther, Hillman D. Holley, John Campbell; the final points of the game came in the fourth on a Hugh Miller run and 33-yard drop kick to make the final score 43–0. Alabama held Howard to only 84 yards on 32 plays; the victory improved Alabama's all-time record against Howard to 11–0. The starting lineup was: Dobbs, Sanford, Whitworth, Elmore, Tucker, H. B. Miller and Boykin; the Tide opened conference play game against the Ole Miss Rebels, for a second consecutive week shutout their opponent. This time the Rebels were defeated 64–0. Alabama's first string entered in the second quarter; the victory improved Alabama's all-time record against Ole Miss to 14–2–1. The starting lineup was: Elmore, Sanford, Leslie, Dothero, H. B. Miller, Tucker and Hanson. For the third week in a row, Alabama shutout its opponent the Sewanee Tigers at Legion Field 25–0.
The team was led by assistant coach Hank Crisp as both head coach Wade and assistant Jess Neely were in Knoxville to scout the Tennessee Volunteers for their game the following week. John Campbell gave Alabama its first points with his 58-yard touchdown run in the second quarter. After Campbell scored his second touchdown, John Tucker scored two more to make the final score 25–0; the victory improved Alabama's all-time record against Sewanee to 13–10–3. The starting lineup was: Elmore, Sanford, Whitworth, Dothero, Miller and Hanson. On homecoming in Tuscaloosa, Alabama defeated coach Robert Neyland's Tennessee Volunteers 18–6 before what was the largest crowd to have seen an Alabama game in Tuscaloosa; the loss was Tennessee's first in 34 games, dating back to a 20–3 loss to Vanderbilt during the 1926 season. The Tide took a 6–0 lead after Johnny Cain scored on a 13-yard touchdown run. John Suther extended their lead to 12–
Burnside-Butler syndrome, is a congenital disorder caused by microdeletion of DNA sequences involving four neurodevelopmental genes. It is associated with a number of psychiatric disorders. More studies are needed to delineate the range of clinical presentation; the 15q11.2 BP1–BP2 microdeletion was the most common cytogenetic abnormality found in a recent study using ultra-high resolution chromosomal microarray analysis optimized for neurodevelopmental disorders of 10,351 consecutive patients presenting for genetic laboratory testing who had autism spectrum disorders. It may represent an under-recognized contributor to the global prevalence of ASD, a common clinical manifestation of many rare genetic disorders, many of which can be identified by chromosome microarray analysis; the 15q11.2 BP1-BP2 microdeletion accounted for 9% of the top 85 genetic findings associated with neurodevelopmental disorders followed by the proximal 16p11.2 deletion syndrome
Alegría Bendayán de Bendelac is a Venezuelan philologist, professor and Jewish poet. During her career she has dedicated to studying sephardic culture the Judeo-Spanish language of northern Morocco, she has been a professor of French at the University of Pennsylvania and has published several works about sephardic traditions. Alegría Bendayán de Bendelac is the fourth of five siblings, daughter of Moroccan immigrants from Tétouan who arrived to Villa de Cura, Aragua state, her parents were Abraham Rachel Cohen of Bendayan. Soon their parents settled in Caracas, she married Rafael Bendelac on June 24, 1953. The couple had two daughters and Lisita. In 1963 she emigrated to New York. Subsequently, she graduated in French at Columbia University and obtained a PhD in French Literature at the same university. After graduating, she began teaching at Fordham University and joined Penn State University. Among her works are dictionaries and historical investigations of Sephardic language and traditions, she has dedicated to writing poetry.
Diccionario del Judeoespañol de Los Sefardíes del Norte de Marruecos Voces Jaquetiescas Los Nuestros. Sejiná, Jaquetía y Fraja. Un retrato de los sefardíes del Norte de Marruecos a través de sus recuerdos y su lengua Structures du rêve et de la realité dans Sylvie Typical Sephardic weddings in Tangier, Morocco Tourmaline II Mosaique: Une enfance juive a Tanger
"The Talented Mr. Rollins" is the third episode of the seventh season of the mystery drama television series Pretty Little Liars, which premiered on July 5, 2016, on the cable network Freeform; the episode was directed by Zetna Fuentes. The episode focuses on the four protagonists trying to find a way to rescue Alison from the psychiatric hospital, during the process, they end up making a terrible, huge mistake. "The Talented Mr. Rollins" was watched by 1.12 million viewers, garnered a 0.5 demo rating, down from the previous episode. This episode is rated TV-14. Emily connects the puzzle pieces as she understands Mary might be working together. Toby and Yvonne get engaged. Spencer feels like breaking up with Caleb because he still loves Hanna. Emily reveals her true feelings to Sabrina. Aria and Hanna find out about Charlotte's love affair; the ladies attempt to rescue Alison from the psychiatric hospital to protect her from Uber A's threats, but in the process, Hanna accidentally hits Elliott with her car, killing him instantly.
The episode was directed by Zetna Fuentes. The episode's title was revealed by Lennon on May 2016, via Twitter; the title is a reference to the 1955 novel The Talented Mr. Ripley by Patricia Highsmith; the table read for this episode occurred in April 25, 2016. Filming started on April 28 and wrapped on May 5, 2016. In the United States, "The Talented Mr. Rollins" was first aired on July 5, 2016, it achieved a viewership of 1.12 million Americans. The episode garnered a 0.5 rating according to Nielsen Media Research. After Live +3 DVR ratings, the episode finished in the fifteenth spot in Adults 18-49, finishing with a 0.9 rating among adults aged 18–49, aired to a total viewership of 1.85 million, placing in the seventeenth spot in viewership. While writing for TV Equals, Mark Trammell gave a favorable review for the episode, saying that it was a "all in all, on okay episode redeemed by that ending." He assumed that Elliott wasn't Uber A, saying that Sara Harvey could be. Jessica Goldstein of Vulture gave the episode 3 out of 5 stars, praised the twist on the plot, commenting: "considering all the gross, sexy-bloody imagery we've had of girls so far this season, it was mighty satisfying/disgusting to watch blood ooze out of Elliot's sad-guppy mouth," and continued, "it was like we were in a time warp back in high school."
"The Talented Mr. Rollins" on IMDb "The Talented Mr. Rollins" at TV.com "The Talented Mr. Rollins" at Freeform.com
Podalic version is an obstetric procedure wherein the fetus is turned within the womb such that one or both feet present through the cervix during childbirth. It is used most in cases where the fetus lies transversely or in another abnormal position in the womb. In modern medicine, abnormal lies are delivered via Caesarean section. According to Gabbe, "There is no place for internal podalic version and breech extraction in the management of transverse or oblique lie or unstable presentation in singleton pregnancies because of the unacceptably high rate of fetal and maternal complications." Podalic version has a long history spanning back to Hippocrates. It fell out of favor over the centuries. Podalic version may be internal. Is internal podalic version a lost art? Optimum mode of delivery in transverse lie Gabbe. Obstetrics: Normal and Problem Pregnancies. 5th Ed. 2007. Churchill Livingstone