1.Maharani Asmara(4101414004) 2.Ika Deavy M(4101414013) 3.Shiyanatussuhailah(4101414015) 4.Arum...
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Transcript of 1.Maharani Asmara(4101414004) 2.Ika Deavy M(4101414013) 3.Shiyanatussuhailah(4101414015) 4.Arum...
![Page 1: 1.Maharani Asmara(4101414004) 2.Ika Deavy M(4101414013) 3.Shiyanatussuhailah(4101414015) 4.Arum Diyastanti(4101414017) 5.Novia Wulan Dary(4101414019) ANGGOTA.](https://reader036.fdocuments.in/reader036/viewer/2022082409/5a4d1b2c7f8b9ab05999976a/html5/thumbnails/1.jpg)
KELOMPOK 1
1. Maharani Asmara(4101414004)
2. Ika Deavy M(4101414013)
3. Shiyanatussuhailah(4101414015)
4. Arum Diyastanti(4101414017)
5. Novia Wulan Dary(4101414019)
ANGGOTA :
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Theorem 7-5
The perpendicular bisectors of the sides of a triangle intersect in a point O that is equidistant from the three vertices of the triangle.
ProofGiven: ABC with perpendicular bisectors 𝜟 l, l’,
and l’’, Proof: l, l’, and l’’ are concurrent in a point O
and that OA = OB = OC.
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A B
C
O
l’
l
L’’
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Statement Reasons
L is the perpendicular bisector of Given
L’ is the perpendicular bisector of Given
L dan L’ intersect in a point O If ∦ then
OA = OB A point a perpendicular bisector is equidistant from the endpoints
OB = OC Why?
OA = OC Transitive property of equality
O is on the perpendicular bisector of A point equidistant from two points is on the perpendicular bisector of the segment determined by those points.
O lies on L, L’, L’’ and OA = OB = OC Statements 4 - 8
L∦L’
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Theorem 7-6
The angle bisectors of the angles of a triangle
are concurrent in a point I that is equidistant from
the three sides of the triangle.
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PROOFGiven : with angle bisectors Prove : are concurrent in a point I that is equidistant from the three sides of the triangle.
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If you were to construct a triangle and its three altitudes, you would see that the lines containing the altitudes are concurrent.
Theorem 7-7The lines that contain the altitudes of a triangle intersect in a point.
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Definition 7-1
A medians of a triangle is a segment joining a
vertex to the midpoint of the opposite side
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Theorem 7-8
The medians of a triangle intersect in a
point that as two thirds of the way from
each vertex to the opposite side
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Theorem 7 - 9
If the measures of two angles of a triangle are unequal, then the length of the side opposite the smaller angle is less than the length of the side opposite the larger angle.
ProofGiven: ABC with m 𝜟 ∠ B < m ∠ AProve: AC < BC
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A B
C
D
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Statement Reasons
m ∠ B < m ∠ A Given
There exists a point D on so that m ∠ BAD = m ∠ B Protractor Postulate
≅ If two angles of a triangle are congruent, then the sides opposite them are congruent
AD = BD Why?
AC < AD + DC Why?
AD + DC = BD + DC Addition of equals property
BD + DC = BC Definition of between for points
AC < BC Substitution Principle
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Theorema 7-10
If the lengths of two sides of a triangles are
unequal then the measure of the angle
opposite the shorter side is less than the
measure of the angle opposite the longer side
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PROOF
Coba kita buat segitiga sembarang, misalnya segitiga
ABC seperti gambar berikut ini.