Triangle Congruence Notes Learning Targets I can recognize
- Slides: 24
Triangle Congruence Notes Learning Targets I can recognize congruent figures and their corresponding parts. I can prove triangles congruent using SSS and SAS. I can prove triangles congruent using ASA and AAS.
Congruence Two geometric figures with exactly the same size and shape.
Corresponding Parts If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Example 1 B 1. AB DE 2. BC EF 3. AC DF 4. A D 5. B E 6. C F A C ABC DEF E F D
Do you need all six ? NO ! SSS SAS ASA AAS
Side-Side or SSS
Side-Side (SSS) B E F A Example 1 1. AB DE 2. BC EF 3. AC DF C D ABC DEF
Included Angle The angle between two sides G I H
Side-Angle-Side or SAS
Side-Angle-Side (SAS) B E F A C 1. AB DE 2. A D 3. AC DF D ABC DEF included angle
Included Side The side between two angles GI HI GH
Included Side Name the included side: E Y S Y and E YE E and S ES S and Y SY
Angle-Side-Angle or ASA
Angle-Side-Angle (ASA) B E F A C 1. A D 2. AB DE D ABC DEF 3. B E included side
Angle-Side or AAS
Angle-Side (AAS) B E F A C 1. A D 2. B E D ABC DEF 3. BC EF Non-included side
Warning: No SSA Postulate There is no such thing as an SSA postulate! E B F A C D NOT CONGRUENT
Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C D NOT CONGRUENT F
The Congruence Postulates F SSS F ASA F SAS F AAS F SSA F AAA
HL (Hypotenuse, Leg) Theorem • Applies only to right triangles • If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.
Name That Postulate (when possible) SAS SSA ASA SSS
Name That Postulate (when possible) AAA SAS ASA SSA
Name That Postulate (when possible) Reflexive Property SAS Vertical Angles SAS Reflexive Property SSA
Let’s Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AC FE For AAS: A F
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