4 2 SSS, SAS, ASA Postulates
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The document outlines three postulates for triangle congruence: the SSS postulate states that if three sides of one triangle are congruent to three sides of another, the triangles are congruent. The SAS postulate specifies that if two sides and the angle between them of one triangle are congruent to those of another, the triangles are congruent. Finally, the ASA postulate describes triangles as congruent if two angles and the side between them are congruent in both triangles.
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This document defines geometric concepts like congruent objects, segments, midpoints, and bisectors. It also introduces angles, describing them as dividing the plane into interior, exterior, and points on the angle. It discusses naming angles using different notation and measuring angles. Finally, it mentions classifying angles by their measures and the important Angle Addition Postulate.
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This document contains a true/false quiz about geometry concepts like lines, planes, and coplanar points. It provides the answers and encourages the reader to re-examine any questions they missed. It then introduces the concept of postulates, or accepted statements without proof, and emphasizes that every word of postulates and theorems is important. It notes that some postulates should be memorized and that the Segment Addition Postulate will be used over 1000 times and should be memorized.
Geo final exam review
This geometry exam review covers topics that will be on the final exam. It includes true/false questions, multiple choice, matching, and free response problems involving geometry concepts like triangles, circles, polygons, and three-dimensional shapes. Calculators may be used but the exam may have non-calculator sections, so students should prepare with and without calculators. The review is due before the scheduled final exam date.
Equations of circles
This document discusses graphing circles and converting between graphing form and standard form equations of circles. It provides examples of writing the equation of a circle given its center and radius in graphing form. It also shows how to find the center, radius, and equation of a circle given the standard form equation. The key points are:
- In graphing form, the center is denoted as (h, k) and the equation is (x - h)2 + (y - k)2 = r2
- To convert to standard form, complete the square and factor the left side, moving any constant to the right side.
6 5 Inequalities in Two Triangles
If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle. Similarly, if two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.
6 4 Inequalities in One Triangle
This document discusses properties of triangles related to side lengths and angles. It states that if one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side. It also states that if one angle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle. The document then asks the reader to identify the longest and shortest sides of a triangle based on these properties.
Chapter 6 and 6-2
This document discusses inequalities and indirect proofs in chapter 6 of a mathematics textbook. It introduces properties of inequalities, such as if a > b and c > 0, then ac > bc. It presents the exterior angle inequality theorem, which states that the measure of an exterior angle of a triangle is greater than the measure of either remote interior angle. It explores how to use properties of inequalities to prove this theorem indirectly. The document also discusses conditional statements and their converses, inverses, and contrapositives. It explains how to use Venn diagrams to represent conditionals and their logical equivalents. Finally, it introduces the law of syllogism for making indirect logical deductions.
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4 2 SSS, SAS, ASA Postulates
- 2. Postulate 12 SSS Postulate – If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. A L R B C – Name the congruence. M
- 3. Postulate 13 SAS Postulate – If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Y N J X Z – Name the congruence. K
- 4. Postulate 14 ASA Postulate – If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. F O T A R – Name the congruence. Y