Triangle Congruence SSS SAS ASA AAS Proving Triangles
![Triangle Congruence SSS, SAS, ASA, & AAS Triangle Congruence SSS, SAS, ASA, & AAS](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-1.jpg)
![Proving Triangles Congruent Proving Triangles Congruent](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-2.jpg)
![The Idea of a Congruence Two geometric figures with exactly the same size and The Idea of a Congruence Two geometric figures with exactly the same size and](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-3.jpg)
![How much do you need to know. . . about two triangles to prove How much do you need to know. . . about two triangles to prove](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-4.jpg)
![Corresponding Parts You learned that if all six pairs of corresponding parts (sides and Corresponding Parts You learned that if all six pairs of corresponding parts (sides and](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-5.jpg)
![Do you need all six ? NO ! SSS SAS ASA AAS Do you need all six ? NO ! SSS SAS ASA AAS](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-6.jpg)
![Side-Side (SSS) Postulate B E F A C 1. AB DE 2. BC EF Side-Side (SSS) Postulate B E F A C 1. AB DE 2. BC EF](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-7.jpg)
![Side-Angle-Side (SAS) Postulate B E F A C 1. AB DE 2. A D Side-Angle-Side (SAS) Postulate B E F A C 1. AB DE 2. A D](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-8.jpg)
![Included Angle The angle between two sides G I H Included Angle The angle between two sides G I H](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-9.jpg)
![Included Angle Name the included angle: E Y S YE and ES E ES Included Angle Name the included angle: E Y S YE and ES E ES](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-10.jpg)
![Angle-Side-Angle (ASA) Postulate B E F A C 1. A D 2. AB DE Angle-Side-Angle (ASA) Postulate B E F A C 1. A D 2. AB DE](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-11.jpg)
![Included Side The side between two angles GI HI GH Included Side The side between two angles GI HI GH](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-12.jpg)
![Included Side Name the included side: E Y S Y and E YE E Included Side Name the included side: E Y S Y and E YE E](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-13.jpg)
![Angle-Side (AAS) Theorem B E F A C 1. A D 2. B E Angle-Side (AAS) Theorem B E F A C 1. A D 2. B E](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-14.jpg)
![Warning: No SSA Postulate There is no such thing as an SSA postulate! E Warning: No SSA Postulate There is no such thing as an SSA postulate! E](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-15.jpg)
![Warning: No AAA Postulate There is no such thing as an AAA postulate! E Warning: No AAA Postulate There is no such thing as an AAA postulate! E](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-16.jpg)
![The Congruence Postulates F SSS correspondence F ASA correspondence F SAS correspondence F AAS The Congruence Postulates F SSS correspondence F ASA correspondence F SAS correspondence F AAS](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-17.jpg)
![Name That Postulate (when possible) Yes, SAS Postulate No, SSA Yes, ASA Postulate Yes, Name That Postulate (when possible) Yes, SAS Postulate No, SSA Yes, ASA Postulate Yes,](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-18.jpg)
![Name That Postulate (when possible) No, AAA Yes, ASA Postulate Yes, SAS Postulate No, Name That Postulate (when possible) No, AAA Yes, ASA Postulate Yes, SAS Postulate No,](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-19.jpg)
![Name That Postulate (when possible) Reflexive Property SAS Vertical Angles SAS Reflexive Property SSA Name That Postulate (when possible) Reflexive Property SAS Vertical Angles SAS Reflexive Property SSA](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-20.jpg)
![HW: Name That Postulate (when possible) HW: Name That Postulate (when possible)](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-21.jpg)
![HW: Name That Postulate (when possible) HW: Name That Postulate (when possible)](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-22.jpg)
![Let’s Practice Indicate the additional information needed to enable us to apply the specified Let’s Practice Indicate the additional information needed to enable us to apply the specified](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-23.jpg)
![HW Indicate the additional information needed to enable us to apply the specified congruence HW Indicate the additional information needed to enable us to apply the specified congruence](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-24.jpg)
![Write a congruence statement for each pair of triangles represented. D B A E Write a congruence statement for each pair of triangles represented. D B A E](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-25.jpg)
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![Slide 1 of 2 Slide 1 of 2](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-27.jpg)
![](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-28.jpg)
![Before we start…let’s get a few things straight C A Y B X INCLUDED Before we start…let’s get a few things straight C A Y B X INCLUDED](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-29.jpg)
![Angle-Side-Angle (ASA) Congruence Postulate Two angles and the INCLUDED side Angle-Side-Angle (ASA) Congruence Postulate Two angles and the INCLUDED side](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-30.jpg)
![Angle-Side (AAS) Congruence Postulate Two Angles and One Side that is NOT included Angle-Side (AAS) Congruence Postulate Two Angles and One Side that is NOT included](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-31.jpg)
![Your Only Ways To Prove Triangles Are Congruent Your Only Ways To Prove Triangles Are Congruent](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-32.jpg)
![Things you can mark on a triangle when they aren’t marked. Overlapping sides are Things you can mark on a triangle when they aren’t marked. Overlapping sides are](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-33.jpg)
![Ex 1 DEF NLM Ex 1 DEF NLM](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-34.jpg)
![Ex 2 What other pair of angles needs to be marked so that the Ex 2 What other pair of angles needs to be marked so that the](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-35.jpg)
![Ex 3 What other pair of angles needs to be marked so that the Ex 3 What other pair of angles needs to be marked so that the](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-36.jpg)
![Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-37.jpg)
![Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-38.jpg)
![Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-39.jpg)
![Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-40.jpg)
![Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-41.jpg)
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![(over Lesson 5 -5) Slide 1 of 2 (over Lesson 5 -5) Slide 1 of 2](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-47.jpg)
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- Slides: 55
![Triangle Congruence SSS SAS ASA AAS Triangle Congruence SSS, SAS, ASA, & AAS](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-1.jpg)
Triangle Congruence SSS, SAS, ASA, & AAS
![Proving Triangles Congruent Proving Triangles Congruent](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-2.jpg)
Proving Triangles Congruent
![The Idea of a Congruence Two geometric figures with exactly the same size and The Idea of a Congruence Two geometric figures with exactly the same size and](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-3.jpg)
The Idea of a Congruence Two geometric figures with exactly the same size and shape. F B A C E D
![How much do you need to know about two triangles to prove How much do you need to know. . . about two triangles to prove](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-4.jpg)
How much do you need to know. . . about two triangles to prove that they are congruent?
![Corresponding Parts You learned that if all six pairs of corresponding parts sides and Corresponding Parts You learned that if all six pairs of corresponding parts (sides and](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-5.jpg)
Corresponding Parts You learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. 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 Do you need all six ? NO ! SSS SAS ASA AAS](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-6.jpg)
Do you need all six ? NO ! SSS SAS ASA AAS
![SideSide SSS Postulate B E F A C 1 AB DE 2 BC EF Side-Side (SSS) Postulate B E F A C 1. AB DE 2. BC EF](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-7.jpg)
Side-Side (SSS) Postulate B E F A C 1. AB DE 2. BC EF 3. AC DF D ABC DEF
![SideAngleSide SAS Postulate B E F A C 1 AB DE 2 A D Side-Angle-Side (SAS) Postulate B E F A C 1. AB DE 2. A D](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-8.jpg)
Side-Angle-Side (SAS) Postulate B E F A C 1. AB DE 2. A D 3. AC DF D ABC DEF included angle
![Included Angle The angle between two sides G I H Included Angle The angle between two sides G I H](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-9.jpg)
Included Angle The angle between two sides G I H
![Included Angle Name the included angle E Y S YE and ES E ES Included Angle Name the included angle: E Y S YE and ES E ES](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-10.jpg)
Included Angle Name the included angle: E Y S YE and ES E ES and YS S YS and YE Y
![AngleSideAngle ASA Postulate B E F A C 1 A D 2 AB DE Angle-Side-Angle (ASA) Postulate B E F A C 1. A D 2. AB DE](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-11.jpg)
Angle-Side-Angle (ASA) Postulate B E F A C 1. A D 2. AB DE D ABC DEF 3. B E included side
![Included Side The side between two angles GI HI GH Included Side The side between two angles GI HI GH](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-12.jpg)
Included Side The side between two angles GI HI GH
![Included Side Name the included side E Y S Y and E YE E Included Side Name the included side: E Y S Y and E YE E](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-13.jpg)
Included Side Name the included side: E Y S Y and E YE E and S ES S and Y SY
![AngleSide AAS Theorem B E F A C 1 A D 2 B E Angle-Side (AAS) Theorem B E F A C 1. A D 2. B E](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-14.jpg)
Angle-Side (AAS) Theorem 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 Warning: No SSA Postulate There is no such thing as an SSA postulate! E](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-15.jpg)
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 Warning: No AAA Postulate There is no such thing as an AAA postulate! E](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-16.jpg)
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 correspondence F ASA correspondence F SAS correspondence F AAS The Congruence Postulates F SSS correspondence F ASA correspondence F SAS correspondence F AAS](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-17.jpg)
The Congruence Postulates F SSS correspondence F ASA correspondence F SAS correspondence F AAS correspondence F SSA correspondence F AAA correspondence
![Name That Postulate when possible Yes SAS Postulate No SSA Yes ASA Postulate Yes Name That Postulate (when possible) Yes, SAS Postulate No, SSA Yes, ASA Postulate Yes,](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-18.jpg)
Name That Postulate (when possible) Yes, SAS Postulate No, SSA Yes, ASA Postulate Yes, SSS Postulate
![Name That Postulate when possible No AAA Yes ASA Postulate Yes SAS Postulate No Name That Postulate (when possible) No, AAA Yes, ASA Postulate Yes, SAS Postulate No,](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-19.jpg)
Name That Postulate (when possible) No, AAA Yes, ASA Postulate Yes, SAS Postulate No, SSA
![Name That Postulate when possible Reflexive Property SAS Vertical Angles SAS Reflexive Property SSA Name That Postulate (when possible) Reflexive Property SAS Vertical Angles SAS Reflexive Property SSA](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-20.jpg)
Name That Postulate (when possible) Reflexive Property SAS Vertical Angles SAS Reflexive Property SSA
![HW Name That Postulate when possible HW: Name That Postulate (when possible)](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-21.jpg)
HW: Name That Postulate (when possible)
![HW Name That Postulate when possible HW: Name That Postulate (when possible)](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-22.jpg)
HW: Name That Postulate (when possible)
![Lets Practice Indicate the additional information needed to enable us to apply the specified Let’s Practice Indicate the additional information needed to enable us to apply the specified](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-23.jpg)
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
![HW Indicate the additional information needed to enable us to apply the specified congruence HW Indicate the additional information needed to enable us to apply the specified congruence](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-24.jpg)
HW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:
![Write a congruence statement for each pair of triangles represented D B A E Write a congruence statement for each pair of triangles represented. D B A E](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-25.jpg)
Write a congruence statement for each pair of triangles represented. D B A E C F
![Slide 1 of 2 Slide 1 of 2](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-26.jpg)
Slide 1 of 2
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Slide 1 of 2
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![Before we startlets get a few things straight C A Y B X INCLUDED Before we start…let’s get a few things straight C A Y B X INCLUDED](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-29.jpg)
Before we start…let’s get a few things straight C A Y B X INCLUDED SIDE Z
![AngleSideAngle ASA Congruence Postulate Two angles and the INCLUDED side Angle-Side-Angle (ASA) Congruence Postulate Two angles and the INCLUDED side](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-30.jpg)
Angle-Side-Angle (ASA) Congruence Postulate Two angles and the INCLUDED side
![AngleSide AAS Congruence Postulate Two Angles and One Side that is NOT included Angle-Side (AAS) Congruence Postulate Two Angles and One Side that is NOT included](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-31.jpg)
Angle-Side (AAS) Congruence Postulate Two Angles and One Side that is NOT included
![Your Only Ways To Prove Triangles Are Congruent Your Only Ways To Prove Triangles Are Congruent](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-32.jpg)
Your Only Ways To Prove Triangles Are Congruent
![Things you can mark on a triangle when they arent marked Overlapping sides are Things you can mark on a triangle when they aren’t marked. Overlapping sides are](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-33.jpg)
Things you can mark on a triangle when they aren’t marked. Overlapping sides are congruent in each triangle by the REFLEXIVE property Vertical Angles are congruent Alt Int Angles are congruent given parallel lines
![Ex 1 DEF NLM Ex 1 DEF NLM](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-34.jpg)
Ex 1 DEF NLM
![Ex 2 What other pair of angles needs to be marked so that the Ex 2 What other pair of angles needs to be marked so that the](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-35.jpg)
Ex 2 What other pair of angles needs to be marked so that the two triangles are congruent by AAS? D L M F E N
![Ex 3 What other pair of angles needs to be marked so that the Ex 3 What other pair of angles needs to be marked so that the](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-36.jpg)
Ex 3 What other pair of angles needs to be marked so that the two triangles are congruent by ASA? D L M F E N
![Determine if whether each pair of triangles is congruent by SSS SAS ASA or Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-37.jpg)
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 4 G K I H J ΔGIH ΔJIK by AAS
![Determine if whether each pair of triangles is congruent by SSS SAS ASA or Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or](https://slidetodoc.com/presentation_image_h2/6f9e774bf2bcf5141d8d32c510c9302a/image-38.jpg)
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 5 B A C D E ΔABC ΔEDC by ASA
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Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 6 E A C B D ΔACB ΔECD by SAS
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Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 7 J M K L ΔJMK ΔLKM by SAS or ASA
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Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 8 J T K L V Not possible U
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Sss sas asa aas
Triangle congruence theorems
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Aaa asa sss
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Congruence postulate
Sss, sas, asa, aas, hl
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Hl
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Shorter
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Sas asa sss
4-3 congruent triangles
4-3 congruent triangles
Lesson 7-3 proving triangles similar
Triangle congruence
Proving triangle congruence
Geometry chapter 4 proving triangle congruence
Triangle similarity aa quiz
Aa triangle similarity
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Triangle similarity: sss and sas assignment
Write whether each pair of triangles are similar
Reflexive property of congruence
Sss congruence postulate examples
Sss congruence
Dr frost congruent triangles
Asa example
7-3 proving triangles similar form g
How to solve a triangle aas
Lesson 7-3 similar triangles answers
Definition of vertical angles proof
Sas congruence postulate
Sas postulate example
How to determine triangle congruence
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