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4.2: Triangle Congruency by SSS and SAS. Objectives: To prove two triangles congruent using the SSS and SAS Postulates. Side-Side-Side (SSS)Postulate. If 3 sides of one triangle are to 3 sides of another triangle, then the triangles are .
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4.2: Triangle Congruency by SSS and SAS Objectives: To prove two triangles congruent using the SSS and SAS Postulates.
Side-Side-Side (SSS)Postulate If 3 sides of one triangle are to 3 sides of another triangle, then the triangles are . (Notice the order in which the congruency statement is given)
B C A D Which other side do we know is congruent? Why? Which two triangles are congruent? 3. How do you know?
Included Angles and Sides N B X is included between Angle B and Angle X is included between NB and NX. Which side is included between angle N and angle B? Which angle is included between BX and NX?
Side-Angle-Side (SAS) Postulate If 2 sides and the included angle of one triangle are to 2 sides and the included angle of another triangle, then the 2 triangles are . Again, notice the order of the congruency statement.
Name the triangle congruence postulate, if any, that you can use to prove each pair of triangles congruent. Then write a congruency statement. K L Q P 1. 2. 3. O M N J M N A S R P C
What other information do you need to prove by SSS? 7 A B 6 8 C D 7 From the information given, can you prove ? Explain. D E B A C
ASA PostulateAngle-Side-Angle • If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
AAS TheoremAngle-Angle-Side • If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.
HL Hypotenuse-Leg If the hypotenuse and a leg of one right triangle are congruent To the hypotenuse and a leg of another right triangle, then The triangles are congruent.
History According to legend, • one of Napoleon’s officers used • congruent triangles to estimate • the width of a river. On the • riverbank, the officer stood up • straight and lowered the visor • of his cap until the farthest thing • he could see was the edge of the • opposite bank. He then turned • and noted the spot on his side • of the river that was in line with • his eye and the tip of his visor.