![]() Using a compass, draw a circle with radius FG and center F. Given a line FG, create a hexagon with side length FG. Same height as each other, thus we know that AE and EB are the same lengths which proves that the line we’ve created is indeed a bisector of line AB.Ĭonstruction 2: Creating a hexagon, given a line We know that congruent triangles must have all the same angles and side lengths as each other since both triangles DAC and DBC have two side lengths equal to DB and one shared side length DC, they both have three identical sides to each other and are thus congruent. This demonstrates that the two triangles DAC and DBC are isosceles.īoth triangles also share the same base DC. Because the circles created on points A and B have the same radius, we know that points D and C are an equal distance away from points A and B, thus DB = BC = CA = AD. If we join the points the following way, one sees that we’ve created two isosceles triangles DAC and DBC. The 2 points of intersection of the two circles will be points onīut how can we prove that this line CD is actually a bisector of line AB? One method is to use congruent triangles to show geometrically that CD must be a bisector of AB. ![]() From the other point B, create a circle with the same radius this time with B as the center point. Extend the compass to create a circle with a radius a little larger than half of length AB and draw the circle. Our first step is to choose point A as the center point for our compass. So all other quadrilaterals are irregular.\) The only regular (all sides equal and all angles equal) quadrilateral is a square. and that's it for the special quadrilaterals. one of the diagonals bisects (cuts equally in half) the other.the diagonals, shown as dashed lines above, meet at.The KiteĮach pair is made of two equal-length sides that join up. (the US and UK definitions are swapped over!)Īn Isosceles trapezoid, as shown above, has left and right sides of equal length that join to the base at equal angles. NOTE: Squares, Rectangles and Rhombuses are allĪ trapezoid (called a trapezium in the UK) has a pair of opposite sides parallel.Īnd a trapezium (called a trapezoid in the UK) is a quadrilateral with NO parallel sides: Also opposite anglesĪre equal (angles "A" are the same, and angles "B" ![]() The ParallelogramĪ parallelogram has opposite sides parallel and equal in length. In other words they "bisect" (cut in half) each other at right angles.Ī rhombus is sometimes called a rhomb or a diamond. The RhombusĪ rhombus is a four-sided shape where all sides have equal length (marked "s").Īlso opposite sides are parallel and opposite angles are equal.Īnother interesting thing is that the diagonals (dashed lines) meet in the middle at a right angle. The SquareĪ square has equal sides (marked "s") and every angle is a right angle (90°)Ī square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length). The little squares in each corner mean "right angle"Ī rectangle is a four-sided shape where every angle is a right angle (90°).Īlso opposite sides are parallel and of equal length. Let us look at each type in turn: The Rectangle Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms. There are special types of quadrilateral: They should add to 360° Types of Quadrilaterals Try drawing a quadrilateral, and measure the angles. interior angles that add to 360 degrees:.(Also see this on Interactive Quadrilaterals) Properties
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