GED 110 - Lesson 4 PDF

3rd YEAR GED 110: TEACHING MATHEMATICS FOR INTERMEDIATE LEARNERS MS. ROWENA S. BONGOLTO, LPT LECTURER MINDANAO STATE UNIVERSITY  OBJECTIVES: IDENTIFIED THE PROPERTIES OF CONGRUENT AND SIMILAR FIGURES PERFORMED RIGID AND SIMILARITY TR...

3rd YEAR GED 110: TEACHING MATHEMATICS FOR INTERMEDIATE LEARNERS MS. ROWENA S. BONGOLTO, LPT LECTURER MINDANAO STATE UNIVERSITY  OBJECTIVES: IDENTIFIED THE PROPERTIES OF CONGRUENT AND SIMILAR FIGURES PERFORMED RIGID AND SIMILARITY TRANSFORMATIONS ON A VARIETY OF FIGURES DISTINGUISHED THE TYPES OF SYMMETRY  ABSTRACTION Geometry of Congruence, Similarity, and Transformations  BASIC GEOMETRIC TERMS CONGRUENT FIGURES SIMILAR FIGURES Congruent figures are identical in both Similar figures have the same shape and size. shape but may differ in size. All corresponding angles and sides of Similarity is often denoted by the congruent figures are equal. symbol ~. Congruence is denoted by the symbol Similar figures can be obtained by ≅. Congruent figures can be obtained by uniformly scaling (enlarging or translating, rotating, or reflecting one reducing) one figure to match the figure onto the other. other.  BASIC GEOMETRIC TERMS RATIO PROPORTION Proportion involves comparing two ratios to A ratio is like a simple way to compare see if they are equal or not. two or more numbers. It tells you how For instance, if we have two rectangles, and one number is related to another. we compare the length to the width for both, For example, if we have a rectangle, and and we find that the ratio of the length to the we want to compare the length of one width is the same for both rectangles, we can side to the length of the other side, we can express this as a ratio. If the length is say they are in proportion. In other words, if 4 CM and the width is 2 CM, we can say Rectangle A has a length-to-width ratio of 3:1, the ratio of the length to the width is 4:2 and Rectangle B has a ratio of 6:2, these ratios are in proportion because both simplify to 3:1.  RATIO VS PROPORTION 6 CM 4 CM 3 CM 2 CM 3 CM LENGTH : 4 CM WIDTH 2 CM RATIO = 4 : 2 1 CM RECTANGLE A = L 6 CM W 3 CM RECTANGLE B = L 3 CM W 1 CM RECTANGLE A - 6 : 3 = 3:1 (LOWEST FORM) RECTANGLE B - 3:1 TOOLS FOR CONSTRUCTING GEOMETRIC FIGURES MIRA A Mira, also known as a geometric mirror or drawing mirror, is a tool used in geometric constructions and drawing to create symmetrical and reflective images. It consists of a reflective surface, typically a mirror, mounted on a board. TOOLS FOR CONSTRUCTING GEOMETRIC FIGURES PAPER FOLDING Paper folding, often known as origami, can be used for basic geometric constructions in a creative and hands-on way. Paper folding is an excellent way to create basic geometric shapes, such as squares, triangles, and rectangles. By folding a piece of paper along specific creases and guidelines, you can form these shapes with precision. TOOLS FOR CONSTRUCTING GEOMETRIC FIGURES COMPASS The primary function of a compass is to draw circles of various sizes. To do this, you adjust the compass's width or radius to the desired measurement and then place the compass's needle point at the center of the circle. In addition to full circles, a compass is used to draw arcs, which are portions of circles. By adjusting the compass to the desired radius, you can draw arcs with precise measurements. TOOLS FOR CONSTRUCTING GEOMETRIC FIGURES STRAIGHTHEDGE The primary purpose of a straightedge is to draw straight lines with precision. It provides a straight and stable edge that you can use as a guide when drawing lines on paper or other surfaces. This is particularly important for creating accurate geometric shapes and diagrams. TOOLS FOR CONSTRUCTING GEOMETRIC FIGURES TECHNOLOGY Technology is increasingly employed in basic construction and geometry-related tasks to enhance precision, efficiency, and accuracy in the creation and manipulation of geometric figures. Online platforms offers interactive lessons, puzzles, and games suitable for kids in learning basic geometry. ABSTRACTION VOLT-IN: FIGURE TRANSFORMATION  Transformations on a variety of figures Transformations on figures involve operations like moving, rotating, reflecting, and resizing shapes. These changes, expressed as mathematical functions, preserve important properties of the figures, such as angles or distances. Studied in geometry, these transformations help understand how shapes can be modified while keeping their essential characteristics TRANSLATION REFLECTION ROTATION DILATION Transformations on a variety of figures TRANSLATION ROTATION Shifting a figure Turning a figure around a horizontally or vertically fixed point by a certain without changing its angle shape or orientation. Transformations on a variety of figures REFLECTION DILATION Flipping a figure over a Enlarging or shrinking a line to create a mirror figure while maintaining image. its shape. PROPERTIES AND OUTCOMES OF RIGID TRANSFORMATIONS Conservation of Distances: Rigid transformations do not change the distances between any two points in the figure. The length of segments and the distance between any pair of points in the original figure remains the same in its transformed counterpart.  PROPERTIES AND OUTCOMES OF RIGID TRANSFORMATIONS 45° Preservation of Angle Measures: The angles between intersecting lines or curves in the original figure are equal to the corresponding angles in the transformed figure. Rigid 90° 45° transformations maintain angle measures. PROPERTIES AND OUTCOMES OF RIGID TRANSFORMATIONS Invariant Shape: The overall shape of the figure is preserved under rigid transformations. The transformed figure is congruent to the original, meaning it has the same size and shape.  PROPERTIES AND OUTCOMES OF RIGID TRANSFORMATIONS II Parallel Lines Remain Parallel: I I II If lines are parallel in the original figure, they remain II parallel after a rigid transformation. Rigid I I II transformations do not alter the parallelism of lines.  ABSTRACTION SAME-MITRY Learning the art of Copy & Paste SYMMETRY Symmetry is a geometric concept that refers to a balanced and harmonious proportionality in the arrangement of parts. In simpler terms, a figure or object is considered symmetrical if it can be divided into two or more identical or mirror- image parts. The line, plane, or point about which the figure is divided is known as the axis or center of symmetry. Symmetry is a fundamental concept in mathematics, art, and nature, and it plays a crucial role in understanding patterns, aesthetics, and structural balance.  TYPES OF SYMMETRY Bilateral Symmetry Radial Symmetry A figure has bilateral symmetry if occurs when a figure can it can be divided into two be divided into identical identical halves by a line such sections, radiating from a that each half mirrors the other. central point.  TYPES OF SYMMETRY Translational Symmetry Rotational Symmetry it can be shifted or translated a figure can be rotated around along a straight line so that the a central point by a certain original and translated positions angle, and it appears are identical. unchanged when rotated.  TYPES OF SYMMETRY Point Symmetry Reflectional Symmetry Also known as central symmetry, Similar to bilateral symmetry, point symmetry occurs when a reflectional symmetry involves figure remains unchanged after a reflecting a figure across a line 180-degree rotation about a to create a mirror image central point. WAYS TO TEACH GEOMETRY TO INTERMEDIATE LEARNERS Visual Aids and Diagrams Use visual aids, charts, and diagrams to illustrate the concepts of congruent figures, similar figures, ratio, proportion, and geometric tools. For example, create a poster with examples of congruent and similar shapes and their corresponding properties. Hands-On Geometry Kits Provide students with geometry kits that include tools like a ruler, compass, protractor, and paper. Encourage them to use these tools to create and measure geometric figures. For instance, students can use a ruler and compass to construct congruent triangles. WAYS TO TEACH GEOMETRY TO INTERMEDIATE LEARNERS Exploring Scale Models Use scale models to demonstrate the concepts of ratio and proportion. For instance, create a scale model of a famous building and discuss how the dimensions are proportionally scaled down. Real-World Applications Connect geometric concepts to real-world applications. For example, use maps to discuss scale and proportions, or analyze architectural blueprints to explore the use of congruent and similar shapes in construction. WAYS TO TEACH GEOMETRY TO INTERMEDIATE LEARNERS Peer Teaching Encourage peer teaching by having students work in pairs or small groups. This can involve explaining concepts to each other or collaborating on a project, like constructing geometric figures using tools. Technology Integration Use educational apps and interactive software to explore geometric concepts. Some apps offer virtual tools for constructing geometric figures, and online quizzes can be used to practice ratio and proportion problems. QUESTIONS?