Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Multilateration wikipedia , lookup
Golden ratio wikipedia , lookup
Perceived visual angle wikipedia , lookup
Euler angles wikipedia , lookup
History of trigonometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Incircle and excircles of a triangle wikipedia , lookup
Euclidean geometry wikipedia , lookup
Regents Geometry Chapter 4 Study Guide Use the following website for on-line resources (practice tests and quizzes): http://www.glencoe.com/sec/math/geometry/geo/geo_04/ Select what you want to do and then go to Chapter 4 Congruent Triangles. Chapter 4 – Congruent Triangles Definitions with images can be found using Quizlet: http://quizlet.com/24476319/flashcards Right Angle Acute Angle Obtuse Angle Acute Triangle Obtuse Triangle Right Triangle Equiangular Triangle Scalene Triangle Isosceles Triangle Equilateral Triangle An angle that measures 90 degrees. An angle that measures between 0 and 90 degrees. An angle that measures between 90 and 180 degrees. A triangle with three acute angles. A triangle with one obtuse angle. A triangle with one right angle. A triangle with three congruent angles. A triangle with no congruent sides. A triangle with at least two congruent sides. A triangle with three congruent sides. Angle Sum Theorem The sum of the measures of the angles of a triangle is 180 degrees. Exterior Angle An angle formed by one side of a triangle and the extension of another side. Remote Interior Angles The angles of a triangle that are not adjacent to a given exterior angle. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Angle Sum Corollary - Acute The acute angles of a right triangle are complementary. That is, they add to 90 degrees. Angle Sum Corollary - Right & Obtuse The can be at most one right angle or one obtuse angle in a triangle. Corresponding Parts Congruent Congruent Polygons CPCTC Third Angle Theorem The matching sides and angles of two figures. Two or more figures that are the same size and shape. Sides are equal in length and angles are equal in measure. Two polygons are congruent if and only if their corresponding parts are congruent. Corresponding Parts of Congruent Triangles are Congruent. If two angle of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. Reflexive Property Symmetric Property Transitive Property ∆ABC ≅ ∆ABC Anything is equal to or congruent to itself. If ∆ABC ≅ ∆EFG, then ∆EFG ≅ ∆ABC. If one quantity equals or is congruent to a second quantity, then the second quantity equals or is congruent to the first. If ∆ABC ≅ ∆ EFG and ∆EFG ≅ ∆JKL, then ∆ABC ≅ ∆JKL. If one quantity equals or is congruent to a second quantity, and the second quantity equals or is congruent to a third quantity, then the first quantity equals or is congruent to the third quantity. SSS (Side-Side-Side) Congruence Included Angle SAS (Side-Angle-Side) Congruence Included Side ASA (Angle-Side-Angle) Congruence AAS (Angle-Angle-Side) Congruence HL (Hypotenuse-Leg) Congruence Legs of an Isosceles Triangle Vertex Angle of an Isosceles Triangle Base Angles of an Isosceles Triangle Isosceles Triangle Theorem If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent. An angle that is included between two sides of a triangle. If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent. A side included between two angles. If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent. If two angles and the non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the right triangles are congruent. The two congruent sides of an isosceles triangle. The angle formed by the legs of an isosceles triangle. The two angles that are not the vertex angle of an isosceles triangle. If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse of Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Equilateral Triangle Property A triangle is equilateral if and only if it is equiangular. Angles of an Equilateral Triangle Each angle of an equilateral triangle measures 60 degrees.