if two altitudes of a triangle are congruent, then the...
TRANSCRIPT
![Page 1: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/1.jpg)
If two altitudes of a triangle are congruent, then the triangle is isosceles.
![Page 2: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/2.jpg)
If two altitudes of a triangle are congruent, then the triangle is isosceles.
![Page 3: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/3.jpg)
If two altitudes of a triangle are congruent, then the triangle is isosceles.
![Page 4: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/4.jpg)
If two altitudes of a triangle are congruent, then the triangle is isosceles.
A
B C
D E
![Page 5: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/5.jpg)
If two altitudes of a triangle are congruent, then the triangle is isosceles.
A
B C
D E
Given: CD and BE are altitudesto AB and AC of ABC.CD BE
Prove: ABC is isosceles.
~=
![Page 6: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/6.jpg)
If two altitudes of a triangle are congruent, then the triangle is isosceles.
A
B C
D E
Given: CD and BE are altitudesto AB and AC of ABC.CD BE
Prove: ABC is isosceles.
~=
Given:
CD BE
Prove:
~=
![Page 7: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/7.jpg)
The medians of a triangle are congruent if the triangle is equilateral.
![Page 8: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/8.jpg)
The medians of a triangle are congruent if the triangle is equilateral.
![Page 9: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/9.jpg)
The medians of a triangle are congruent if the triangle is equilateral.
![Page 10: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/10.jpg)
The medians of a triangle are congruent if the triangle is equilateral.
A
B C
D E
F
![Page 11: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/11.jpg)
The medians of a triangle are congruent if the triangle is equilateral.
A
B C
D E
Given:
Prove:
Given:
Prove:
F
![Page 12: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/12.jpg)
The medians of a triangle are congruent if the triangle is equilateral.
A
B C
D E
Given: AF, BE, and CD are all medians of equilateral ABC
Prove:
Given:
Prove:
F
![Page 13: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/13.jpg)
The medians of a triangle are congruent if the triangle is equilateral.
A
B C
D E
Given: AF, BE, and CD are all medians of equilateral ABC
Prove:
Given:
Prove:
F
![Page 14: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/14.jpg)
The medians of a triangle are congruent if the triangle is equilateral.
A
B C
D E
Given: AF, BE, and CD are all medians of equilateral ABC
Prove:
Given: D is midpoint of AB F is midpoint of BC E is midpoint of AC
Prove:
F
![Page 15: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/15.jpg)
The medians of a triangle are congruent if the triangle is equilateral.
A
B C
D E
Given: AF, BE, and CD are all medians of equilateral ABC
Prove:
Given: D is midpoint of AB F is midpoint of BC E is midpoint of AC
Prove:
F
![Page 16: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/16.jpg)
The medians of a triangle are congruent if the triangle is equilateral.
A
B C
D E
Given: AF, BE, and CD are all medians of equilateral ABC
Prove:
Given: D is midpoint of AB F is midpoint of BC E is midpoint of AC
Prove:
F
![Page 17: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/17.jpg)
The altitude to the base of an isosceles triangle bisects the vertex angle.
![Page 18: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/18.jpg)
The altitude to the base of an isosceles triangle bisects the vertex angle.
Given:
Prove:
Given: Prove:
![Page 19: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/19.jpg)
The altitude to the base of an isosceles triangle bisects the vertex angle.
Given:
Prove:
Given: Prove:
![Page 20: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/20.jpg)
The altitude to the base of an isosceles triangle bisects the vertex angle.
A
B C
Given:
Prove:
D
Given: Prove:
![Page 21: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/21.jpg)
The altitude to the base of an isosceles triangle bisects the vertex angle.
A
B C
Given: Isosceles ABC with vertex BAC and
altitude AD to side BC Prove:
D
Given: Prove:
![Page 22: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/22.jpg)
The altitude to the base of an isosceles triangle bisects the vertex angle.
A
B C
Given: Isosceles ABC with vertex BAC and
altitude AD to side BC Prove: AD bisects BAC
D
Given: Prove:
![Page 23: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/23.jpg)
The altitude to the base of an isosceles triangle bisects the vertex angle.
A
B C
Given: Isosceles ABC with vertex BAC and
altitude AD to side BC Prove: AD bisects BAC
D
Given: Prove:
![Page 24: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/24.jpg)
The altitude to the base of an isosceles triangle bisects the vertex angle.
A
B C
Given: Isosceles ABC with vertex BAC and
altitude AD to side BC Prove: AD bisects BAC
D
Given: Prove:
![Page 25: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/25.jpg)
The altitude to the base of an isosceles triangle bisects the vertex angle.
A
B C
Given: Isosceles ABC with vertex BAC and
altitude AD to side BC Prove: AD bisects BAC
D
Given: Prove: BAD CAD ~=
![Page 26: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/26.jpg)
If two angles of one triangle are congruent to two angles of another triangle, the remaining
pair of angles are also congruent.
![Page 27: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/27.jpg)
If two angles of one triangle are congruent to two angles of another triangle, the remaining
pair of angles are also congruent.
![Page 28: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/28.jpg)
If two angles of one triangle are congruent to two angles of another triangle, the remaining
pair of angles are also congruent.
![Page 29: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/29.jpg)
If two angles of one triangle are congruent to two angles of another triangle, the remaining
pair of angles are also congruent.
A
B
CD
FE
![Page 30: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/30.jpg)
If two angles of one triangle are congruent to two angles of another triangle, the remaining
pair of angles are also congruent.
A
B
CD
FE
![Page 31: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/31.jpg)
If two angles of one triangle are congruent to two angles of another triangle, the remaining
pair of angles are also congruent.
A
B
CD
FE
![Page 32: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/32.jpg)
If two angles of one triangle are congruent to two angles of another triangle, the remaining
pair of angles are also congruent.
A
B
CD
Given: Prove:
FE
![Page 33: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/33.jpg)
If two angles of one triangle are congruent to two angles of another triangle, the remaining
pair of angles are also congruent.
A
B
CD
Given: Prove:
FE
![Page 34: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/34.jpg)
If two angles of one triangle are congruent to two angles of another triangle, the remaining
pair of angles are also congruent.
A
B
CD
Given: Prove:
FE
![Page 35: If two altitudes of a triangle are congruent, then the ...tcanright.webmate.me/Geometry_Channel/Part_4g/Part... · The altitude to the base of an isosceles triangle bisects the vertex](https://reader035.vdocument.in/reader035/viewer/2022081615/5fdcba0cdcdc2d050f34f24a/html5/thumbnails/35.jpg)
In this lesson we drew diagrams for problems presented
with words.