warm up: solve for x
DESCRIPTION
Warm up: Solve for x. Linear Pair. 4x + 3 . 7x + 12. X = 15. Special Segments in Triangles. Median. Connect vertex to opposite side's midpoint. Altitude. Connect vertex to opposite side and is perpendicular. Tell whether each red segment is an altitude of the triangle. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/1.jpg)
Warm up: Solve for x.Warm up: Solve for x.Linear Pair
4x + 3 7x + 12
X = 15
![Page 2: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/2.jpg)
Special Special Segments in Segments in
TrianglesTriangles
![Page 3: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/3.jpg)
MedianMedian
![Page 4: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/4.jpg)
AltitudeAltitude
![Page 5: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/5.jpg)
Tell whether each red segment is an altitude of the triangle.The altitude is the “true
height” of the triangle.
![Page 6: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/6.jpg)
Perpendicular Perpendicular BisectorBisector
![Page 7: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/7.jpg)
Tell whether each red segment is an perpendicular bisector of the triangle.
![Page 8: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/8.jpg)
Angle BisectorAngle Bisector
![Page 9: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/9.jpg)
Start to Start to memorizememorize…
•Indicate the special triangle segment based on its description
![Page 10: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/10.jpg)
I cut an angle into two equal parts
![Page 11: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/11.jpg)
I connect the vertex to the opposite side’s
midpoint
![Page 12: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/12.jpg)
I connect the vertex to the opposite side and
I’m perpendicular
![Page 13: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/13.jpg)
I go through a side’s midpoint and I am
perpendicular
![Page 14: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/14.jpg)
Drill & PracticeDrill & Practice•Indicate which special triangle segment the red line is based on the picture and markings
![Page 15: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/15.jpg)
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q1:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
![Page 16: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/16.jpg)
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q2:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
![Page 17: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/17.jpg)
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q3:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
![Page 18: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/18.jpg)
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q4:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
![Page 19: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/19.jpg)
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q5:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
![Page 20: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/20.jpg)
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q6:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
![Page 21: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/21.jpg)
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q7:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
![Page 22: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/22.jpg)
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q8:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
![Page 23: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/23.jpg)
Points of Points of ConcurrencyConcurrency
![Page 24: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/24.jpg)
New VocabularyNew Vocabulary(Points of (Points of
Intersection)Intersection)1. Centroid2. Orthocenter3. Incenter4. Circumcenter
![Page 25: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/25.jpg)
Point of Point of IntersectionIntersection
intersect at the
![Page 26: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/26.jpg)
Important Info about the Centroid
• The intersection of the medians.• Found when you draw a segment from one
vertex of the triangle to the midpoint of the opposite side.
• The center is two-thirds of the distance from each vertex to the midpoint of the opposite side.
• Centroid always lies inside the triangle. • This is the point of balance for the triangle.
![Page 27: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/27.jpg)
The intersection of the medians is called the CENTROID.
![Page 28: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/28.jpg)
Point of Point of IntersectionIntersection
intersect at the
![Page 29: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/29.jpg)
Important Info about the Orthocenter
• This is the intersection point of the altitudes.• You find this by drawing the altitudes which is
created by a vertex connected to the opposite side so that it is perpendicular to that side.
• Orthocenter can lie inside (acute), on (right), or outside (obtuse) of a triangle.
![Page 30: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/30.jpg)
The intersection of the altitudes is called the ORTHOCENTER.
![Page 31: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/31.jpg)
Point of Point of IntersectionIntersection
intersect at the
![Page 32: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/32.jpg)
Important Info about the Incenter
• The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.
• Incenter is equidistant from the sides of the triangle.
• The center of the triangle’s inscribed circle.• Incenter always lies inside the triangle
![Page 33: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/33.jpg)
The intersection of the angle bisectors is called the INCENTER.
![Page 34: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/34.jpg)
Point of Point of IntersectionIntersection
intersect at the
![Page 35: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/35.jpg)
Important Information about the Circumcenter
• The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.
• The circumcenter is the center of a circle that surrounds the triangle touching each vertex.
• Can lie inside an acute triangle, on a right triangle, or outside an obtuse triangle.
![Page 36: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/36.jpg)
The intersection of the perpendicular bisector is called the CIRCUMCENTER.
![Page 37: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/37.jpg)
Memorize these!Memorize these!MCAOABI
PBCC
Medians/Centroid
Altitudes/Orthocenter
Angle Bisectors/Incenter
Perpendicular Bisectors/Circumcenter
![Page 38: Warm up: Solve for x](https://reader036.vdocuments.mx/reader036/viewer/2022081604/56814685550346895db3a6bb/html5/thumbnails/38.jpg)
Will this work?Will this work?MCAOABI
PBCC
My Cousin
Ate Our
Avocados But I
Prefer Burritos Covered in Cheese