PPT-4-5 Isosceles and Equilateral

Triangles LEQ How do you use and apply properties of isosceles triangles to solve problems Parts of an Isosceles Triangle Between the 2 legs Surround the base If 2 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 In Perspective. Symmetry and Regularity. Objects that are symmetrical look the same from several different views, or two sides are mirror images of each other.. Symmetric solids are referred to as regular, or Platonic solids.. Raymond Flood. Gresham Professor of Geometry. Overview. Group of Symmetries of the equilateral triangle. Compare the group of symmetries of a square and a rectangle. Symmetries of the platonic solids. Takeshi Tokuyama. Tohoku University. Joint work with many collaborators. Prologue: balancing in real life. 　　　. C. enter of mass. and barycenter. Given a set of weighted points q(. i. Which is the correct definition of isosceles?. a.) a triangle with at least 2 congruent sides. b.) a triangle with exactly 2 congruent sides. 4.5 Isosceles Triangles. LEQ: How can we use properties of isosceles triangles to construct proofs?. 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. with . Understanding. **This is meant as a resource to the teacher! It is NOT intended to replace teaching in the classroom OR the discourse that should take place!!. Inscribing in a Circle . Inscribe a Hexagon in a Circle. Geometry Module 3-1 Isosceles Right Triangle Reflections Overview: of squares through isosceles right triangles. Objective: TExES Mathematics Competencies III.012.D. The beginning teacher uses proper Sec: 4.6. 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. Leg. th. Grade. TRIANGLES. Triangles. A polygon with three sides. Is the simplest of the polygons. Formed by three straight lines. The interior angles add up to 180 degrees. Exterior angles add up to 360 degrees.. Triangles. Isosceles Triangles. leg. leg. base. Vertex angle. Base angle. Base angle. 2 sides are congruent. 2 theorems. If 2 sides are congruent, then base angles are congruent. If 2 . base angles . and. . 4.2/1-10. Lessons 4.1 and 4.2 . Triangle Sum Properties & Properties of Isosceles Triangles. -. Classify triangles and find measures of their angles.. - Discover the properties of Isosceles 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.)..