Chapter 12 (Sp12)

# Chapter 12 (Sp12) - Section 12-1 Congruence Through...

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Section 12-1 – Congruence Through Constructions Congruence versus Similarity In mathematics, similar objects have the same shape but not necessarily the same size. Congruent objects have the same size and they are similar. Two line segments are only congruent if they have the same length. Two angles are only congruent if they have the same measure. Circle : the set of all points in a plane that are the same distance (radius) from a given point (center). Arc: any part of the circle that can be drawn without lifting a pencil. (can be major or minor) If the major and minor arcs are the same size, then each is a semicircle. The center of the arc is the center of the circle containing the arc. Triangle Congruence: B B′ A C A′ C′ SSS Property: If the three sides of one triangle are congruent, respectively, to the three sides of a second triangle, then the two triangles are congruent. 1

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SAS Property: If two sides and the included angle of one triangle are congruent to two sides and the included angles of another triangle, respectively, then the two triangles are congruent. Examples : Determine if the following pairs of triangles are congruent. A Statement Reason B C E D F Statement Reason 120° 120° HL Property: If the hypotenuse and leg of one right triangle are congruent, respectively, to the hypotenuse and leg of another right triangle, then the two triangles are congruent. 2
A line that is perpendicular to a segment and bisects it is the perpendicular bisector of the line segment. Theorems:

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## This note was uploaded on 01/06/2012 for the course MATH 1351 taught by Professor Lisajuliano during the Spring '12 term at Collins.

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Chapter 12 (Sp12) - Section 12-1 Congruence Through...

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