1 / 14

4.2: Triangle Congruency by SSS and SAS

This educational material provides a thorough exploration of how to prove triangle congruency using the Side-Side-Side (SSS) and Side-Angle-Side (SAS) postulates. It outlines the conditions under which two triangles are considered congruent through specific side and angle arrangements. Including practical examples, this text encourages students to identify congruent triangles and apply the relevant congruency postulates. Historical context is also provided, illustrating the real-world application of these geometric principles.

garron
Télécharger la présentation

4.2: Triangle Congruency by SSS and SAS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 4.2: Triangle Congruency by SSS and SAS Objectives: To prove two triangles congruent using the SSS and SAS Postulates.

  2. 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)

  3. B C A D Which other side do we know is congruent? Why? Which two triangles are congruent? 3. How do you know?

  4. 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?

  5. 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.

  6. 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

  7. 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

  8. 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.

  9. 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.

  10. Can you prove the triangles are congruent?

  11. 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.

  12. Can you prove the triangles are congruent?

  13. 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.

More Related