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This document provides formulas and examples for calculating areas and properties of basic plane geometric shapes like triangles, parallelograms, trapezoids, circles, and polygons. It includes 9 cases for calculating triangle area using different known properties like base/altitude, two sides/included angle, or all three sides.
Triangle A triangle is a closed figure in a plane consisting of three segments called sides. Any two sides intersect in exactly one point called a vertex. A triangle is named using the capital letters assigned to its vertices in a clockwise or counterclockwise direction. For example, the triangle below can be named triangle ABC in a
Chapter 1. SIMILAR TRIANGLES 15 Background 15 Introductory problems 15 §1. Line segments intercepted by parallel lines 15 §2. The ratio of sides of similar triangles 17 §3. The ratio of the areas of similar triangles 18 §4. Auxiliary equal triangles 18 * * * 19 §5. The triangle determined by the bases of the heights 19 §6. Similar figures 20
1) What is the name of a triangle where all sides have different lengths? 2) A triangle has sides of length 8 and 13. What are the possible lengths of the 3rd side?
The sides of a triangle are 21, 20 and 13cm respectively, find the area of the triangles into which it is divided by the perpendicular upon the longest side from the opposite angular point.
1. Introduction to plane geometry In this Chapter we review some elementary plane geometry. We assume that the notions of isosceles triangles, parallel lines, similar triangles, area, etc. are already familiar. We will review the deflnitions of medians, angle bisectors, perpendicular bisectors and altitudes, and
In a plane, 2 lines that are perpendicular to a common line are parallel. Two lines that are perpendicular to a common line must be parallel. A triangle is always a planar figure. A square is always a planar figure. Two lines must intersect or be parallel. If a line is perpendicular to a plane, it is perpendicular to every line in that plane.
