GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.
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Transcript of GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.
![Page 1: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/1.jpg)
GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable
Bellringer P 23 top 10 lines
![Page 2: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/2.jpg)
Triangle Congruence
Sections 4-2, 4-3, 4-6
![Page 3: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/3.jpg)
SSS
![Page 4: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/4.jpg)
Example
![Page 5: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/5.jpg)
NOTE:
• The only time two sides are unmarked and congruent are when they are shared sides (like in the previous example)
• This is because of the Reflexive property of congruence
![Page 6: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/6.jpg)
SAS
![Page 7: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/7.jpg)
Note:
• The congruent angle MUST BE between the two congruent sides.
• The only time unmarked angles are congruent is when they are vertical (they make the X)
![Page 8: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/8.jpg)
Try it
![Page 9: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/9.jpg)
Again
![Page 10: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/10.jpg)
Bellringer
![Page 11: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/11.jpg)
ASA
![Page 12: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/12.jpg)
NOTE:
• The congruent side needs to be between the congruent angles.
![Page 13: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/13.jpg)
![Page 14: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/14.jpg)
AAS
![Page 15: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/15.jpg)
NOTE
• The third angles theorem states that when two angles of a triangle are congruent to two angles of a different triangle then the third angles are also congruent.
• This connects AAS to ASA
![Page 16: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/16.jpg)
Example:
![Page 17: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/17.jpg)
WRITING A PROOF FOR TRIANGLE CONGRUENCE
![Page 18: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/18.jpg)
RIGHT TRIANGLES
![Page 19: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/19.jpg)
HL
![Page 20: GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.](https://reader035.fdocuments.us/reader035/viewer/2022062300/56649f575503460f94c7b43c/html5/thumbnails/20.jpg)
NOTE:
• This only works for right triangles• MUST have congruent hypotenuses• MUST have a pair of congruent legs
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Example