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7-1 Points, Lines, and Planes Learn to describe figures by using the terms of geometry. Course 1 7-1 Points, Insert Lesson TitlePlanes Here Lines, and Vocabulary point line plane line segment ray Course 1 7-1 Points, Lines, and Planes The building blocks of geometry are points, lines, and planes. A point is an exact location. P point P, A point is named by a capital letter. A line is a straight path that extends without end in opposite directions. AB A B BA A line is named by two points on the line. A plane is a flat surface that extends without end in all directions. L M N plane LMN, plane MLN, plane NLM A plane is named by three points on the plane that are not on the same line. Course 1 7-1 Points, Lines, and Planes A line segment is a line made of two endpoints and all the points between the endpoints. X XY YX Y A line segment is named by its endpoints. A ray has one endpoint. From the endpoint, the ray extends without end in one direction only. J K ray JK, JK A ray is named by its endpoint first followed by another point on the ray. Course 1 7-5 Triangles Learn to classify triangles and solve problems involving angle and side measures of triangles. Course 1 7-5 Triangles Insert Lesson Title Here Vocabulary acute triangle obtuse triangle right triangle scalene triangle isosceles triangle equilateral triangle Course 1 7-5 Triangles A triangle is a closed figure with three line segments and three angles. Triangles can be classified by the measures of their angles. An acute triangle has only acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle. Acute triangle Course 1 Obtuse triangle Right triangle 7-5 Triangles To decide whether a triangle is acute, obtuse, or right, you need to know the measures of its angles. The sum of the measures of the angles in any triangle is 180°. You can see this if you tear the corners from a triangle and arrange them around a point on a line. By knowing the sum of the measures of the angles in a triangle, you can find unknown angle measures. Course 1 7-5 Triangles Additional Example 1: Application Sara designed this triangular trophy. The measure of E is 38°, and the measure of F is 52°. Classify the triangle. To classify the triangle, find the measure of D on the trophy. E D F m D = 180° – (38° + 52°) m D = 180° – 90°Subtract the sum of the known angle measures m D = 90° from 180° So the measure of D is 90°. Because DEF has one right angle, the trophy is a right triangle. Course 1 7-5 Triangles Triangles can be classified by the lengths of their sides. A scalene triangle has no congruent sides. An isosceles triangle has at least two congruent sides. An equilateral triangle has three congruent sides. Course 1 7-5 Triangles Try This: Example 3 Classify the triangle. The sum of the lengths of the sides is 21.6 in. B d + (7.2 + 7.2) = 21.6 d + 14.4 = 21.6 7.2 in. 7.2 in. d + 14.4 – 14.4 = 21.6 – 14.4 d = 7.2 A d Side d is 7.2 inches long. Because ABC has three congruent sides, it is equilateral. Course 1 C 7-5 Triangles Insert Lesson Title Here Lesson Quiz If the angles can form a triangle, classify the triangle as acute, obtuse, or right. 1. 37°, 53°, 90° right acute 3. 61°, 78°, 41° 2. 65°, 110°, not25° a triangle obtuse 4. 115°, 25°, 40° The lengths of three sides of a triangle are given. Classify the triangle. scalene 5. 12, 16, 25 6. 10, 10, 15 Course 1 isosceles 7-6 Quadrilaterals Learn to identify, classify, and compare quadrilaterals. Course 1 7-6 Quadrilaterals Insert Lesson Title Here Vocabulary quadrilateral parallelogram rectangle rhombus square trapezoid Course 1 7-6 Quadrilaterals A quadrilateral is a plane figure with four sides and four angles. Five special types of quadrilaterals and their properties will be shown in this lesson. The same mark on two or more sides of a figure indicates that the sides are congruent. Course 1 7-6 Quadrilaterals Parallelogram Rectangle Course 1 Opposite sides are parallel and congruent. Opposite angles are congruent. Parallelogram with four right angles. 7-6 Quadrilaterals Rhombus Square Course 1 Parallelogram with four congruent sides. Rectangle with four congruent sides. 7-6 Quadrilaterals Trapezoid Course 1 Quadrilateral with exactly two parallel sides. May have two right angles. 7-6 Quadrilaterals Insert Lesson Title Here Lesson Quiz Complete each statement. 1. A quadrilateral with four right angles is a _________. square or rectangle ? 2. A parallelogram with four right angles and four congruent sides is a _______. ? square 3. A figure with 4 sides and 4 angles is a ______. ? quadrilateral 4. Give the most descriptive name for this quadrilateral. trapezoid Course 1 7-7 Polygons Learn to identify regular and not regular polygons and to find the angle measures of regular polygons. Course 1 7-7 Polygons Insert Lesson Title Here Vocabulary polygon regular polygon Course 1 7-7 Polygons Triangles and quadrilaterals are examples of polygons. A polygon is a closed plane figure formed by three or more line segments. A regular polygon is a polygon in which all sides are congruent and all angles are congruent. Polygons are named by the number of their sides and angles. Course 1 7-7 Polygons Course 1 7-7 Polygons Additional Example 1A: Identifying Polygons Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular. A. The shape is a closed plane figure formed by 3 or more line segments. polygon There are 5 sides and 5 angles. pentagon All 5 sides do not appear to be congruent. Not regular Course 1 7-7 Polygons Additional Example 1B: Identifying Polygons Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular. B. The shape is a closed plane figure formed by 3 or more line segments. polygon There are 8 sides and 8 angles. octagon The sides and angles appear to be congruent. regular Course 1 7-11 Symmetry Learn to identify line symmetry. Course 1 7-11 Symmetry Insert Lesson Title Here Vocabulary line symmetry line of symmetry Course 1 7-11 Symmetry A figure has line symmetry if it can be folded or reflected so that the two parts of the figure match, or are congruent. The line of reflection is called the line of symmetry. Course 1 7-11 Symmetry Additional Example 1A: Identifying Lines of Symmetry Determine whether each dashed line appears to be a line of symmetry. A. The two parts of the figure appear to match exactly when folded or reflected across the line. The line appears to be a line of symmetry. Course 1 7-11 Symmetry Additional Example 1B: Identifying Lines of Symmetry Determine whether each dashed line appears to be a line of symmetry. B. The two parts of the figure do not appear congruent. The line does not appear to be a line of symmetry. Course 1 7-11 Symmetry Try This: Example 1B Determine whether each dashed line appears to be a line of symmetry. B. The two parts of the figure appear to match exactly when folded or reflected across the line. The line appears to be a line of symmetry. Course 1 7-11 Symmetry Some figures have more than one line of symmetry. Course 1 7-11 Symmetry Additional Example 2A: Finding Multiple Lines of Symmetry Find all of the lines of symmetry in the regular polygon. A. Trace the figure and cut it out. Fold the figure in half in different ways. Count the lines of symmetry. 5 lines of symmetry Course 1 7-11 Symmetry Additional Example 3A: Social Studies Application Find all of the lines of symmetry in the flag. A. Alaska There are no lines of symmetry. Course 1 7-11 Symmetry Additional Example 3B: Social Studies Application Find all of the lines of symmetry in the flag. B. Arizona 1 line of symmetry Course 1 7-11 Symmetry Additional Example 3C: Social Studies Application Find all of the lines of symmetry in the flag. C. Colorado 1 line of symmetry Course 1 7-11 Symmetry Additional Example 3D: Social Studies Application Find all of the lines of symmetry in the flag. D. New Mexico 2 lines of symmetry Course 1 7-11 Symmetry Try This: Example 3A Find all of the lines of symmetry in each design. 2 lines of symmetry Course 1 7-11 Symmetry Try This: Example 3B Find all of the lines of symmetry in each design. There are no lines of symmetry. Course 1 7-11 Symmetry Try This: Example 3C Find all of the lines of symmetry in each design. 1 line of symmetry Course 1 7-11 Symmetry Insert Lesson Title Here Lesson Quiz Does the described figure have line symmetry? 1. right isosceles triangle yes 2. rectangle yes Do the following capital letters of the alphabet have symmetry? If so, is the line of symmetry horizontal or vertical? 3. H yes, vertical and horizontal Course 1 4. R no