* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download File
Survey
Document related concepts
Perspective (graphical) wikipedia , lookup
Tessellation wikipedia , lookup
History of geometry wikipedia , lookup
Penrose tiling wikipedia , lookup
Multilateration wikipedia , lookup
Dessin d'enfant wikipedia , lookup
Technical drawing wikipedia , lookup
Golden ratio wikipedia , lookup
Euler angles wikipedia , lookup
Apollonian network wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Reuleaux triangle wikipedia , lookup
History of trigonometry wikipedia , lookup
Incircle and excircles of a triangle wikipedia , lookup
Euclidean geometry wikipedia , lookup
Transcript
Geometry Final Study Guide Chapter 3 Review Things You Should Know Triangle Congruency Postulates Different Types of Segments Types of Triangles Other Useful Theorems QuickTime™ and a decompressor are needed to see this picture. SSS Postulate If there exists a correspondence between the vertices of two triangles such that three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent Tick marks show congruent parts QuickTime™ and a decompressor are needed to see this picture. ASA Postulate If there exists a correspondence between the vertices of two triangles such that two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent It is illegal to use ASA to prove triangles congruent if the congruent side is not between the two congruent angles QuickTime™ and a decompressor are needed to see this picture. SAS Postulate If there exists a correspondence between the vertices of two triangles such that two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent Remember, the congruent angle must be between the two congruent sides to use this postulate QuickTime™ and a decompressor are needed to see this picture. Home HL Postulate If there exists a correspondence between the vertices of two right triangles such that the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle, the two right triangles are congruent If you know two sides of one right triangle are congruent to two sides of another right triangle, then you can prove the right triangles congruent no matter where the sides are positioned QuickTime™ and a decompressor are needed to see this picture. Types of Segments QuickTime™ and a decompressor are needed to see this picture. Auxiliary lines: Lines that are not drawn in on the original diagram that the “proover” draws in himself/herself These lines are represented as dotted lines Median: A line segment drawn from any vertex of the triangle to the midpoint of the opposite side Every triangle has three medians Home Types of Segments Cont. Altitude: A line segment drawn from any vertex of the triangle to the opposite side Every triangle has three altitudes In an isosceles triangle, the median drawn from the vertex angle to the base of the triangle is also the altitude of the triangle QuickTime™ and a decompressor are needed to see this picture. Types of Triangles QuickTime™ and a decompressor are needed to see this picture. Equilateral triangle: All sides are congruent Equiangular triangle: All angles are congruent Equiangular triangles and equilateral triangles are the same Isosceles triangle: Triangle in which at least two sides are congruent Home Types of Triangles Cont. QuickTime™ and a decompressor are needed to see this picture. Acute triangle: A triangle in which all angles are acute Obtuse triangle: A triangle in which one of the angles is obtuse Right triangle: One of the angles of this type of triangle is a right angle A triangle cannot have more than one obtuse angle QuickTime™ and a decompressor are needed to see this picture. Qui ckTime™ and a decompressor are needed to see thi s pi cture. CPCTC Stands for, “Corresponding Parts of Congruent Triangles are Congruent” Example: Two congruent triangles were proved congruent by SAS These triangles will be known as triangle ABC and triangle XYZ CPCTC Cont. Because the two triangles are congruent, the corresponding sides AB and XY are congruent as well QuickTime™ and a decompressor are needed to see this picture. Radii Theorem All radii of a circle are congruent A radius is a segment that extends from the center of the circle to any point on the circle This theorem is very useful in proofs such as these, where triangles are inside circles. QuickTime™ and a decompressor are needed to see this picture. Angle-Side Theorems If two sides of a triangle are congruent, the angles opposite the sides are congruent Can be shortened to “If sides, the angles” when used in a proof QuickTime™ and a decompressor are needed to see this picture. Angle-Side Theorems Cont. Home If two angles of a triangle are congruent, the sides opposite the angles are congruent Can be shortened to “If angles, then sides” when used in proofs QuickTime™ and a decompressor are needed to see this picture.