KELOMPOK 1

1. Maharani Asmara(4101414004)

2. Ika Deavy M(4101414013)

3. Shiyanatussuhailah(4101414015)

4. Arum Diyastanti(4101414017)

5. Novia Wulan Dary(4101414019)

ANGGOTA :

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.

A B

C

O

l’

l

L’’

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’

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.

PROOFGiven : with angle bisectors Prove : are concurrent in a point I that is equidistant from the three sides of the triangle.

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.

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.

ProofGiven: ABC with m 𝜟 ∠ B < m ∠ AProve: AC < BC

A B

C

D

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

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.