Transcript
![Page 1: The Triangle Inequality Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side](https://reader036.vdocument.in/reader036/viewer/2022082713/5697bfeb1a28abf838cb7a72/html5/thumbnails/1.jpg)
The Triangle Inequality
Triangle Inequality Theorem
• The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
![Page 2: The Triangle Inequality Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side](https://reader036.vdocument.in/reader036/viewer/2022082713/5697bfeb1a28abf838cb7a72/html5/thumbnails/2.jpg)
Determine whether the given measures can be lengths of the sides of a triangle.
a. 6, 9, 16
b. 14, 16, 27
Answer: no
Answer: yes
![Page 3: The Triangle Inequality Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side](https://reader036.vdocument.in/reader036/viewer/2022082713/5697bfeb1a28abf838cb7a72/html5/thumbnails/3.jpg)
A 4 B 9 C 12 D 16
Answer: D
Multiple-Choice Test ItemWhich measure cannot
be XZ?
![Page 4: The Triangle Inequality Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side](https://reader036.vdocument.in/reader036/viewer/2022082713/5697bfeb1a28abf838cb7a72/html5/thumbnails/4.jpg)
The Triangle Inequality
Theorem 5.12• The perpendicular segment from a point to
a line is the shortest segment from the point to the line.
Corollary 5.1• The perpendicular segment from a point to
a plane is the shortest segment from the point to the plane.
![Page 5: The Triangle Inequality Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side](https://reader036.vdocument.in/reader036/viewer/2022082713/5697bfeb1a28abf838cb7a72/html5/thumbnails/5.jpg)
Prove: AB > AD
Given: is an altitude in ABC.