![]() ![]() In an isosceles triangle, the bisector of the vertex angle, The line containing the bisector of the vertex angle These can also be described as the angles at the endpoints of the base.Ĭertain terms will be defined further below. The two angles opposite the equal sides are the base angles (and are equal). The side opposite the vertex angle is called the base. ![]() The angle determined by the two equal sides There are special names associated with the angles and sides ofĪn isosceles triangle. Just as there are special names associated with the sides of Note: a right/acute/obtuse triangle might be either scalene or isosceles.Īlso, our definition of isosceles includes and does not exclude the Or by the largest angle (acute, right, obtuse).Ī hierarchy chart combining both situations is given at the left.ĭue to the overlap, hierarchy charts for either situation (0 is scalene, 2 or more is isosceles, all 3 is equilateral) Symmetric Triangles (Isosceles and Equilateral) The function y= x 2 defines a parabola in which These symmetries will be useful when applied to various polygons. Rorschach inkblots and logos commonly are reflective-symmetric. If a figure is symmetric, then any pair of corresponding parts The section concludes with the following important result. The semicircles are reflections of each other). (no matter which way you draw the diameter, This is the same as the letter I discussed above.Īngles only have one line of symmetry: the angleīisector which causes one ray to reflect onto the other ray.Ī circle has infinitely many lines of symmetry Our textbook states and proves what they call theįlip-Flop Theorem: (reflection is symmetric). Them into a crossword puzzle (for extra credit)! Of letters with a vertical line of symmetry.Īfter collecting enough of these words you might make Or MOM, WAXY, YOUTH (written vertically!) composed entirely There may be more than one line of symmetry.Ī challenge would be to find words such as DIXIE or COOKBOOKĬomposed entirely of letters with a horizontal line of symmetry Whereas others are symmetric about a vertical line (AHIMOTUVWXY).Īs you can see since some are in both lists (HIOX), Some are symmetric about a horizontal line (BCDEHIKOX) The capital letters A, B, C, D, E, H, I, K, M, O, T, U, V, W, X, and YĪre often written as reflection symmetric figures. This line is a symmetry line for the figure. If and only if there is a line which reflects the figure onto itself. Noether's Theorem, Homework Reflection-Symmetric Figures.Incenter, Circumcenter, Orthocenter, and Centroid.Hierarchy of Triangles, Symmetric Triangles (Isosceles, Equilateral).The capital letters H, I ,O and X all have both horizontal and vertical line symmetry.Īll the rest of the letters (F, G, J, K, L, N, P, Q, R, S and Z) have no line symmetry.Symmetry and Polygons Back to the Table of Contents A Review of Basic Geometry - Lesson 6 Classifying Polygons by Symmetry Lesson Overview It would be easy to draw a capital B that did have horizontal line symmetry-this one almost does. I can't tell that without actually flipping it upside down or measuring, though, so I left it in my list. ![]() Actually, even though I included B (and maybe you did too), B isn't perfectly symmetric in the Arial font because the top loop of the B is just a tiny bit smaller than the bottom loop. I see horizontal line symmetry in the captial letters B, C, D, E, H, I, O and X. I see vertical line symmetry in the capital letters A, H, I, M, O, T, U, V, W, X and Y (some of these have other kinds of symmetry too!) Even among san serif fonts, symmetry can be slightly different, so my answers may be different from yours if I write my letters differently. Arial is a san serif font-all of those extra bits are missing in an Arial font-that makes the letters have more symmetry. I'm using the Arial font, which is a san-serif font. Serifs are the little fancy bits on the ends of letters: Times is a serif font-f's have little lines at the bottom, and S's have little lines at the top and bottom, and A is thinner on the left side than the right side. It all depends on just how you draw your letters. Introduction to Symmetry Line symmetry in capital letters ![]()
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