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
Noether's theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
Rational trigonometry wikipedia , lookup
Line (geometry) wikipedia , lookup
History of trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Integer triangle wikipedia , lookup
Euler angles wikipedia , lookup
Four color theorem wikipedia , lookup
Tensors in curvilinear coordinates wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Euclidean geometry wikipedia , lookup
Quadrilaterals and Coordinates Proof Opening routine If the figure is a parallelogram. Solve for x. Topic IV: Quadrilaterals and Coordinate Proof Quadrilaterals and Coordinates Proof Objective: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent Essential Question: How can properties of parallelograms be used to find missing sides and/or angles? Quadrilaterals and Coordinates Proof Vocabulary Parallelogram: Is a quadrilateral with two pairs of parallel sides. Rectangle: Is a quadrilateral with four right angles. Rhombus: Is a simple quadrilateral whose four sides all have the same length. Square: A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. Quadrilaterals and Coordinates Proof Vocabulary Trapezoid: Is a quadrilateral that has a pair of opposite sides parallel. The sides that are parallel are called “bases”. Isosceles trapezoid: Is a special type of trapezoid in which non-parallel sides and base angles are equal. Kite: Is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. Quadrilaterals and Coordinates Proof Classification of Quadrilaterals Quadrilaterals and Coordinates Proof Properties of Parallelograms Quadrilaterals and Coordinates Proof Properties of Parallelograms Quadrilaterals and Coordinates Proof Properties of Parallelograms Quadrilaterals and Coordinates Proof Properties of Parallelograms Guided Practice – WE DO Quadrilaterals and Coordinates Proof Properties of Parallelograms Guided Practice – WE DO Quadrilaterals and Coordinates Proof Properties of Parallelograms Quadrilaterals and Coordinates Proof Properties of Parallelograms Guided Practice – WE DO Quadrilaterals and Coordinates Proof Properties of Parallelograms Guided Practice – WE DO Quadrilaterals and Coordinates Proof Properties of Parallelograms Independent Practice - YOU DO Worksheet Properties of Parallelograms Exercises from 1 to 10 Quadrilaterals and Coordinates Proof Properties of Parallelograms Closure Essential Question: How can properties of parallelograms be used to find missing sides and/or angles? Quadrilaterals and Coordinates Proof Properties of Parallelograms Exit Ticket A quadrilateral is a parallelogram if any one of the following is true. Both pairs of opposite sides are __________and _________. Both pairs of opposite angles are ___________. Diagonals ____________ each other. A pair of opposite sides is both ________and _________. Quadrilaterals and Coordinates Proof Re-teach MAFS.912.G-SRT.2.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Math Nation Section 5 Topic 3 Independent Practice Quadrilaterals and Coordinates Proof Re-teach MAFS.912.G-CO.3.9: Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Math Nation Section 3 Topic 7 Independent Practice Quadrilaterals and Coordinates Proof Re-teach MAFS.912.G-CO.3.10: Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Math Nation Section 4 Topic 3 Independent Practice