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ANGGOTA :
1.
2.
3.
4.
5.
Maharani Asmara
(4101414004)
Ika Deavy M
(4101414013)
Shiyanatussuhailah
(4101414015)
Arum Diyastanti
(4101414017)
Novia Wulan Dary
(4101414019)
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.
Proof
Given: 𝜟 ABC with perpendicular bisectors l, l’,
and l’’,
Proof: l, l’, and l’’ are concurrent in a point O
and that OA = OB = OC.
C
L’’
l’
A
O
l
B
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
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
∦
then
L∦L’
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.
PROOF
Given : ∆𝐴𝐵𝐶with angle bisectors 𝑙, 𝑙 ′ 𝑎𝑛𝑑 𝑙 ′′ .
Prove : 𝑙, 𝑙 ′ 𝑎𝑛𝑑 𝑙 ′′ are concurrent in a point I that
is equidistant from the three sides of the triangle.
𝑙
𝑙′
𝑙 ′′
If you were to construct a triangle and its three
altitudes, you would see that the lines containing
the altitudes are concurrent.
Theorem 7-7
The lines that contain the
altitudes of a triangle intersect
in a point.
Definition 7-1
A medians of a triangle is a segment joining a
vertex to the midpoint of the opposite side
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
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.
Proof
Given: 𝜟 ABC with m ∠ B < m ∠ A
Prove: AC < BC
C
D
A
B
Statement
Reasons
m∠B<m∠A
There exists a point D on
∠ BAD = m ∠ B
≅
Given
so that m
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
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
PROOF
Coba kita buat segitiga sembarang, misalnya segitiga
ABC seperti gambar berikut ini.