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Transcript
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: π ABC with perpendicular bisectors l, lβ, and lββ, Proof: l, lβ, and lββ are concurrent in a point O and that OA = OB = OC. C Lββ lβ A O l B Statement Reasons L is the perpendicular bisector of Given Lβ is the perpendicular bisector of Given L dan Lβ 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, Lβ, Lββ and OA = OB = OC Statements 4 - 8 β¦ then Lβ¦Lβ 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 : βπ΄π΅πΆwith angle bisectors π, π β² πππ π β²β² . Prove : π, π β² πππ π β²β² are concurrent in a point I that is equidistant from the three sides of the triangle. π πβ² π β²β² 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: π ABC with m β B < m β A Prove: AC < BC C D A B Statement Reasons mβ B<mβ A There exists a point D on β BAD = m β B β 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.