* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Congruent Triangles
Survey
Document related concepts
Lie sphere geometry wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Noether's theorem wikipedia , lookup
Analytic geometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Penrose tiling wikipedia , lookup
Dessin d'enfant wikipedia , lookup
History of geometry wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
Technical drawing wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
Apollonian network wikipedia , lookup
Trigonometric functions wikipedia , lookup
Euler angles wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Transcript
Congruent Triangles Chapter 4-3 Standard 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. Congruent Triangles • Two triangles are congruent if all of their corresponding sides and corresponding angles are congruent. Y Congruent Triangles B ABC YXZ C A Congruent Angles A Y X Order is important!!! Congruent Sides AB YX B X BC XZ C Z AC YZ Z Corresponding Congruent Parts B. ARCHITECTURE A tower's roof is composed of congruent triangles all converging toward a point at the top. Name the congruent triangles. Answer: ΔHIJ ΔKIL Corresponding Congruent Parts A. ARCHITECTURE A tower's roof is composed of congruent triangles all converging toward a point at the top. Name the corresponding congruent angles and sides of A. The support beams on the fence form congruent triangles. Which of the following congruence statements directly matches corresponding angles or sides ΔABC and ΔDEF? A. B. C. D. B. The support beams on the fence form congruent triangles. Which statement correctly names the congruent triangles? A. ΔACB ΔEDF B. ΔCBA ΔFED C. ΔBCA ΔDFE D. ΔBAC ΔEFD B Third Angles Theorem C E F A • If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. If A D and B E, then C F. D Congruence Properties • Reflexive Property of Every triangle is congruent to itself • Symmetric Property of If ABC DEF, then DEF ABC. • Transitive Property of If ABC DEF, and DEF JKL, then ABC JKL. Transformations in the Coordinate Plane A. COORDINATE GEOMETRY The vertices of are R(─3, 0), S(0, 5), and T(1, 1). The vertices of ST are R(3, 0), S(0, ─5), and T(─1, ─1). Use the Distance Formula to find the length of each side of the triangles. Transformations in the Coordinate Plane Transformations in the Coordinate Plane Homework Chapter 4-3 • Pg 220: 6-9 10-13 use the distance formula to show that the sides are congruent 20, 25-28, 39-41