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Transcript
Journal Chapter 6 FRANCIS MIFSUD T2 _____(0-10 pts.) Describe what a polygon is. Include a discussion about the parts of a polygon. Also compare and contrast a convex with a concave polygon. Compare and contrast equilateral and equiangular. Give 3 examples of each. Polygons: polygons are closed figures made of 3 or more straight lines. Polygons include sides, vertices, and diagonals Sides: the sides are the points that meet at vertices. Vertices: they are where the sides of the polygon meet Diagonals: they are the imaginary lines that go from one of the vertices to the opposite angles. Concave Concave polygons are those who have an interior angle that is more than 180 degrees. (angles push in) Concave polygon The Yellow angle make these polygons concave Convex Convex is when no interior angles are larger than 180 degrees (no angles push in) No angles are larger than 180 degrees which makes the polygons convex Equiangular Equiangular are seen in many places like in boxes and stop signs STO P Equilaterals Equilaterals are used in many square objects like rhombuses. _____(0-10 pts.) Explain the Interior angles theorem for quadrilaterals. Give at least 3 examples. The interior angles theorem for quadrilaterals works like this…. How many sides are there? Then subtract 2 from the # of sides… Then multiply by 180 to find the degrees of the quadrilateral! (4-2)180= 360 The theorem says that (n-2)180… n being the number of sides. (4-2)180=360 (4-2)180=360 Describe the 4 theorems of parallelograms and their converse and explain how they are used. Give at least 3 examples of each. When one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram Converse: it is a parallelogram if if a pair of opposite sides are congruent and parallel. This is an easy way to see if a quadrilateral is a parallelogram because you only need to find the length of the sides and if their they are perp. To each other then you can see they are parallel Second Theorem When both pairs of opposite sides of quadrilaterals are congruent the quadrilateral is a parallelogram Converse: It is a parallelogram if both of the opposite sides are congruent. This is easy to use because if you know all the lengths you can find if it is a parallelogram Third… When an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram Converse: it is a parallelogram if the angle is supplementary to both of its consecutive angles. If the meeting angles are supplementary then they it is a parallelogram This is helpful because sometimes you are given the angles and you can see if they are supplementary Fourth… When the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram Converse: It is a parallelogram if the diagonals bisect each other Describe how to prove that a quadrilateral is a parallelogram. Include an explanation about theorem 6.10. Give at least 3 examples of each First you have to know the definition of Quadrilateral is a 4 sided figure. And that a parallelogram has many properties to it Def.: 4 sided figure with 2 sets of parallel line 1. First you have need to know that opposite angles are congruent 2. Second you need find one pair of sides are parallel and congruent 3. Then show that diagonals Bisect 4. Then show that adjacent/ Consecutive angles are supplementary 5. At last with theorem 6.10 that states that if a quadrilateral is a parallelogram then its opposite sides are congruent, show that it is a parralelogram Compare and contrast a rhombus with a square with a rectangle. Describe the rhombus, square and rectangle theorems. Give at least 3 examples of each Square: All Sides are Right Angles Equilateral and Equiangular Diagonals Bisect Diagonals are Perpendicular Adjacent/Consecutive Angles are supplementary Rhombus: All sides are congruent Diagonals are Perpendicular Rectangles: A parallelogram with 4 right angles All angles are right angles Diagonals are Congruent Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3 examples of each. A trapezoid is a quadrilateral with 2 base sides that are parallel to each other Some properties of a trapezoid are: 1. Both pairs of base angles are congruent 2. A quadrilateral with one pair of parallel lines 3. Diagonals are Congruent Theorems of a Trapezoid Isosceles- Legs or 2 non parallel sides are congruent Midsegment Formula b1+b2/2 Describe a kite. Explain the kite theorems. Give at least 3 examples of each. A Kite is composed of two figures tor two triangles that make a polygon with bisecting diagonals Properties: One Pair of congruent opposite angles One pair of congruent opposite sides. Longer Diagonal bisects the shorter diagonal (Perpendicular) Theorems Theorems: If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. If a quadrilateral is a kite, then its diagonals are perpendicular Describe how to find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples of each. Trapezoid: A= a (b1 + b2) /2 a is the altitude Rhombus: base times height Parallelograms: baste time height Rectangle/ Square: base times height Kite : area of top triangle plus area of bottom triangle Triangle: base times height /2