Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of...
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Transcript of Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of...
![Page 1: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.](https://reader036.fdocuments.us/reader036/viewer/2022082511/5a4d1b937f8b9ab0599c2725/html5/thumbnails/1.jpg)
Name the angles opposite of each side:
X is opposite of YZY is opposite of XZZ is opposite of XY
X
Y
Z
![Page 2: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.](https://reader036.fdocuments.us/reader036/viewer/2022082511/5a4d1b937f8b9ab0599c2725/html5/thumbnails/2.jpg)
Triangle Inequalities
GeometryMrs. King
Unit 4, Day 5
![Page 3: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.](https://reader036.fdocuments.us/reader036/viewer/2022082511/5a4d1b937f8b9ab0599c2725/html5/thumbnails/3.jpg)
Triangle Inequality Theorem
• The sum of the length of any two sides of a triangle is greater than the third side.
• XY + YZ > XZ• YZ + XZ > XY• XZ + XY > YZ
X
Y
Z
![Page 4: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.](https://reader036.fdocuments.us/reader036/viewer/2022082511/5a4d1b937f8b9ab0599c2725/html5/thumbnails/4.jpg)
Using the Triangle Inequality Theorem…
• Is it possible for 3, 7, and 8 to be the sides of a triangle?
![Page 5: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.](https://reader036.fdocuments.us/reader036/viewer/2022082511/5a4d1b937f8b9ab0599c2725/html5/thumbnails/5.jpg)
Using the Triangle Inequality Theorem…
• What about 3, 6, and 10?
![Page 6: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.](https://reader036.fdocuments.us/reader036/viewer/2022082511/5a4d1b937f8b9ab0599c2725/html5/thumbnails/6.jpg)
Inequalities Relating Sides and Angles
• Theorem 4-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.
• Ex. If XZ > XY,then mY > mZ
X
Y
Z
![Page 7: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.](https://reader036.fdocuments.us/reader036/viewer/2022082511/5a4d1b937f8b9ab0599c2725/html5/thumbnails/7.jpg)
Inequalities Relating Sides and Angles
• Theorem 4-11: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.
• Ex. If mY > mZ,then XZ > XY
X
Y
Z
![Page 8: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.](https://reader036.fdocuments.us/reader036/viewer/2022082511/5a4d1b937f8b9ab0599c2725/html5/thumbnails/8.jpg)
In TUV, Name the sides from shortest to longest
• TV, UV, UT
6258U V
T
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Homework
Work Packet:Triangle Inequalities