PPT-Section 4.5 isosceles & equilateral triangles

Geometry Legs are congruent Isosceles Triangle Vertex Angle Base Angles Legs Theorem 43 Isosceles Triangle Thm If two sides of a triangle are congruent then the angles opposite those sides are congruent. Equilateral Triangles Figure 1 Recall the wellknown theorem of van Schooten Theorem 1 If ABC is an equilateral triangle and is a point on the arc BC of ABC then MA MB MC Proof Use Ptolemy on the cyclic quadrilater Classifying Triangles by Angles. ACUTE. OBTUSE. RIGHT. EQUIANGULAR. ACUTE TRIANGLE. All interior angles are acute (or have a measure less than 90°). Interior Angle. Example of Acute Triangle. Phineas’s. The ability to copy and bisect angles and segments, as well as construct perpendicular and . parallel lines. , allows you to construct a variety of geometric figures, including triangles, squares, . and hexagons. Sec: . 4.5. Sol: G.5. Properties of Isosceles Triangles. An isosceles triangle is a triangle with two congruent sides.. The congruent sides are called legs and the third side is called the base.. 3. “. Cogito ergo sum.”. -- Rene Descartes, . Discourse on the Method. . real mathematics. “Mathematics. , rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. Helpful websites. http://www.regentsprep.org/Regents/mathb/1c/preprooftriangles.htm. http://www.mathwarehouse.com/geometry/congruent_triangles/. http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Congruent-Triangles.topicArticleId-18851,articleId-18788.html. Polygon: A closed plane figure with 3 or more sides (line segments) that intersect only at the endpoints.. Vertex: Each endpoint of a side of a polygon.. Convex Polygon: A polygon such that . no line. Warm Up. 1. . Find each angle measure.. True or False. If false explain.. 2.. Every equilateral triangle is isosceles.. 3.. Every isosceles triangle is equilateral.. . 60°; 60°; 60°. True. False; an isosceles triangle can have only two congruent sides.. Objective. :. To understand and apply properties of isosceles and equilateral triangles.. Supplies. :. Math Notebook. Assignment: 4.8 p. 276: 1-10, 12-16, 22-26. 4.8: Isosceles & Equilateral Triangles. CCSS. Content Standards. G.CO.10 Prove theorems about triangles. . G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).. Lewis Carroll/Charles Dodgson. Some . fun facts:. .. as a mathematician, Dodgson was, in the words of . . Peter Heath: "An inveterate publisher of trifles [who] was forever putting out pamphlets, papers, broadsheets, and books on mathematical topics [that] earned him no reputation beyond that of a crotchety, if sometimes amusing, controversialist, a compiler of puzzles and curiosities, and a busy yet ineffective reformer on elementary points of computation and instructional method. In the higher reaches of the subject he made no mark at all, and has left none since." . Geometry. 5.1 Angles of Triangles. Essential Question. How are the angle measures of a triangle related?. 5.1 Angles of Triangles. November 21, 2016. 5.1 Angles of Triangles. November 21, 2016. Goals – . Chapter 4. This Slideshow was developed to accompany the textbook. Larson Geometry. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. of a trapezoid. :. __________________________________________________. __________________________________________________.  . The . parallel sides are called ________________________. . The . nonparallel sides are called ________________. .