Topic 4 Quadrilaterals and Coordinate Proof

Transcript:Topic 4 Quadrilaterals and Coordinate Proof:
Topic 4 Quadrilaterals and Coordinate Proof Geometry Vocabulary Choose 3-4 vocabulary words for the day. Throughout the lesson, as students respond to your questions or are presenting a problem on the board, mark a tally when a vocabulary word is used accurately. This can be turned into a competition among groups or between periods. Mathematically Speaking! Examples of accuracy line vs line segment translation vs slide midpoint vs the middle Quadrilateral A four-sided polygon. Quadrilaterals Flowchart Properties of Parallelograms Opposite sides are parallel and congruent. Opposite angles are congruent. Consecutive angles are supplementary. The diagonals bisect each other. Rectangle A rectangle is a parallelogram with four right angles. Diagonals are congruent. Diagonals bisect each other. All the properties of a parallelogram apply by definition. Rhombus A rhombus is a parallelogram with four congruent sides. Diagonals are perpendicular bisectors of each other Each diagonal bisects a pair of opposite angles. The diagonals divide the rhombus into four congruent angles All the properties of a parallelogram apply by definition. Square All the properties of a rectangle apply by definition. All squares are rectangles All the properties of a rhombus apply by definition. All squares are rhombuses The diagonals form four isosceles right triangles. Coordinate Geometry Proofs Proving a triangle is a Right Triangle Proving a Quadrilateral is a Parallelogram Method 4: Show one pair of sides is both parallel and equal. Proving a Quadrilateral is a Rectangle Proving a Quadrilateral is a Rhombus Trapezoid A trapezoid is a quadrilateral with exactly one pair of parallel sides. Isosceles trapezoid – A trapezoid where the two base angles are equal and therefore the sides opposite the base angles are also equal. The legs are congruent by definition. The bases are parallel by definition. The base angles are congruent. The diagonals are congruent. Any lower base angle is supplementary to any upper base angle Enrichment