Conditions for Triangle Congruence - CABT Grade 8

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Information about Conditions for Triangle Congruence - CABT Grade 8
Education

Published on February 25, 2014

Author: gjnabueg

Source: slideshare.net

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Lecture on Conditions on Triangle Congruence for Grade 8 - Assumption at CABT

Conditions for Triangles Congruence

The Idea of a Congruence Two geometric figures with exactly the same size and shape. F B A C E D Conditions for Triangle Congruence

How much do you need to know. . . . . . about two triangles to prove that they are congruent? Conditions for Triangle Congruence

Corresponding Parts In the previous lesson, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. 1. AB  DE 2. BC  EF 3. AC  DF 4.  A   D ABC   DEF 5.  B   E 6.  C   F Conditions for Triangle Congruence

QUESTION! Do you need all six ? NO ! Conditions for Triangle Congruence

The Conditions for Triangle Congruence SSS SAS ASA SAA Side, Side, Side Congruence Postulate Side, Angle, Side Congruence Postulate Angle, Side, Angle Congruence Postulate Side, Angle, Angle Congruence Theorem Woohoo… Conditions for Triangle Congruence

Side-Side-Side (SSS) Corresponding Sides are Congruent 1. AB  DE 2. BC  EF ABC   DEF 3. AC  DF Conditions for Triangle Congruence

Side-Angle-Side (SAS) 1. AB  DE 2. A   D ABC   DEF 3. AC  DF included angle Two corresponding sides and corresponding included angles are congruent

Included Angle The angle between two sides G I H Conditions for Triangle Congruence

Included Angle Name the included angle: E YE and ES ES and YS Y S E S YS and YE Y Conditions for Triangle Congruence

Angle-Side-Angle (ASA) 1. A   D 2. AB  DE ABC   DEF 3.  B   E included side Two corresponding angles and corresponding included sides are congruent

Included Side The side between two angles GI HI GH Conditions for Triangle Congruence

Included Side Name the included side: E Y and E E and S Y S YE ES S and Y SY Conditions for Triangle Congruence

Side-Angle-Angle (SAA) 1. A   D 2.  B   E ABC   DEF 3. BC  EF Two corresponding angles and corresponding non-included sides are congruent Non-included side

Warning: No SSA Postulate There is no such thing as an SSA postulate! E B F A C D NOT CONGRUENT Conditions for Triangle Congruence

Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C D F NOT CONGRUENT Conditions for Triangle Congruence

Check your understanding Name that Condition! If the triangles are congruent, identify the condition that justifies the congruence. If not, state that they are not congruent SAS SSA not congruent ASA SSS

Check your understanding Name that Condition! If the triangles are congruent, identify the condition that justifies the congruence. If not, state that they are not congruent AAA not congruent SAS ASA not congruent SSA

Check your understanding Name that Condition! If the triangles are congruent, identify the condition that justifies the congruence. If not, state that they are not congruent Reflexive Property SAS Vertical Angles SAS Vertical Angles SAS Reflexive Property SSA not congruent

Seatwork Name that Condition! If the triangles are congruent, identify the condition that justifies the congruence. If not, state that they are not congruent (3) (1) (2) (4)

Seatwork Name that Condition! If the triangles are congruent, identify the condition that justifies the congruence. If not, state that they are not congruent (6) (5) (7)

Let’s Practice Indicate the additional information needed to enable to apply the specified congruence postulate. For ASA: B  D For SAS: AC  FE For SAA: A  F

Check your understanding Indicate the additional information needed to enabble to apply the specified congruence postulate. For ASA: For SAS: For SAA:

Conditions for Triangle Congruence

The Congruence Conditions  SSS congruence  ASA congruence  SAS congruence  SAA congruence  SSA congruence  AAA congruence Conditions for Triangle Congruence

Thank Thank you! you!

Acknowledgement This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching. Revisions made by Mr. Gilbert Joseph Abueg, February 18, 2014

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