It should also be noted that the shortest distance between a point and a
This definition works whether or not the polygon is convex. The next in the order specified, otherwise its orientation is Hand is toward the interior as you proceed from one vertex to Polygons are said to have a clockwise orientation if your right This doubly reflected image is now directly congruent with If in turn the image is reflected again, orientation reverses again. This corresponds with another name for reflection: flip.Ī figure and its reflection are termed oppositely congruent. If you are facing east and looking in a mirror, your reflected image In addition to the ABCD properties listed above which are preserved, This allows you to then quickly locate image points. It has a squared base andįlat surface which extends perpendicular to the paper. We suggest using differently colored pencilsĪ MIRA device is a semitransparent plastic tool which This tells us how to locate and draw an image given its corresponding preimage. Perpendicular bisector of segment PQ (assuming points The line of reflection is always halfway between correspondingĪ point Q is the reflected image of point P The surface of the water is the line of (symmetry) reflection. Think of a pond reflecting the landscape. The line of reflection or reflecting line is where the Refers to the corresponding image points. If points on the image are labelled, then an apostrophe after the label Preimage and the copied version as the image.
We refer to the original figure (you) as the When you raise your right hand, the mirrored What do you see when looking in the mirror? The exactĬopy of your figure but reversed. We will discuss the four isometries in detail next. It combines the symbolism of equality (=) and If and only if G is the image of F under an isometry. Two figures F and G are congruent figures, Some purists define congruence as follows. There are only four transformations which are isometries.Īnother name for an isometry is a congruence transformation. (Our textbook elevates this to theorem status,īut a careful look at its foundation might be revealing.)īreaking the word isometry down into its root pieces indicates These can easily be remembered by their first letter sequence: ABCD. Specifically, Angle measure, Betweenness, Collinearity,Īnd Distance are preserved by all isometries. Similar mappings can be done with sets of points or figures.Ĭertain properties of a figure are preserved by some transformations.įormally these are contained in a Reflection Postulate. Particular mapping can be inverted: x = ½( y - 1).) Specifies how each value of x corresponds with y. Y = 2 x + 1 maps x into y and the equation Transformation from one variable to another. ( one-to-one) and each point in the image must have exactly one Mean any problem which severely tests the ability of anĬongruence means to have the same shape and measure.Ī transformation is a mapping (correspondence) between points.Įach point in the preimage must have a unique image point (then sides are equal) known as Pons Asinorum, Triangle Theorem (then base angles are equal) or its converse The alternative is to adopt something like SAS triangleĮither will be at the heart of a proof of the Isosceles To guarantee their inverse is a function can perhaps be best Specifically, the notation of forming the composition of functions Various branches of higher mathematics are simplified by aīasic understanding of the symbolism and terminology of such mappings. In fact, further study in high school mathematics and especially Through the use of transformations and isometries.
Many modern high school geometry textbooks, including UCSMP, Homework Transformations, Congruent Transformations, Isometries.Practical Applications: Miniature Golf and Billiards.Transformations, Congruent Transformations, Isometries.Back to the Table of Contents A Review of Basic Geometry - Lesson 4 Mirror, Mirror : Reflections and Congruence Lesson Overview Find a point on the line of reflection that creates a minimum distance.Mirror, Mirror.Determine the number of lines of symmetry.Describe the reflection by finding the line of reflection.Where should you park the car minimize the distance you both will have to walk? You need to go to the grocery store and your friend needs to go to the flower shop. Now we all know that the shortest distance between any two points is a straight line, but what would happen if you need to go to two different places?įor example, imagine you and your friend are traveling together in a car. And did you know that reflections are used to help us find minimum distances?