Plane figures
Mathematics, Grade 8
Plane figures
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Study Guide Plane figures Mathematics, Grade 8
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PLANE FIGURES What Are Plane Figures? Plane figures refer to points, lines, angles, and planes in the coordinate plane. A figure that is three-dimensional has points on many different planes. Lines can be parallel or perpendicular. Angles can be categorized as acute, obtuse or right. Angles can also be complementary or supplementary depending on how many degrees they add up to. Plane figures can also refer to shapes in the coordinate plane. Triangles, quadrilaterals and other polygons can be shown in the coordinate plane. How to use plane figures In the coordinate plane, points can be plotted and figures can be drawn. If a line is drawn, it must contain two points. Any two points on a line can name the line. Lines can be parallel, which means that they will never cross, or perpendicular, which means that two lines meet at right angles. Lines can also be drawn to make angles. Lines can cross to form adjacent angles, which are next to each other, vertical angles, which are across from each other, complementary angles, which add up to 90° and supplementary angles, which add up to 180°. Angles can be acute, 90°; o r right = 90°. Triangles are classified based on the measure of the angle within it. If two angles of a triangle are given, the third can be found by subtracting the sum of the two angles given from 180°. In a quadrilateral, the angles add up to 360°. In a polygon with n sides, the sum of the interior angles = (n - 2) · 180°. If given 3 angles of a quadrilateral, the fourth angle can be found by subtracting the known angles from 360°. If angles consist of variables, the measures of the angles can be found by solving for x and substituting back into the equation for each angle. For example, what is the measure of the angle A? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Ex. <A + <B + <C = 180 (x - 21) + (2x + 4) + (x + 25) = 180 4x + 8 = 180 4x = 172, x = 43° Since x = 43°, the measure of <A = 22°. Any angles can be found this way when the angles contain variables. A regular polygon is a polygon that has equal angles and equal sides. The measure of each interior angle of a regular polygon is (n - 2)(180°)/n. Try This! 1. If angle 1 and angle 2 are supplementary and angle 1 is 112°, what is the measure of angle 2? 2. A triangle has two angles that measure 54° and 45°, what type of triangle is it? 3. For the figure shown, what is the measure of each angle? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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