Isosceles Triangle (Theorem) 6. The median to the base of an isosceles triangle is theperpendicular bisector of the base.RESTATEMENTGiven: Isosceles triangle ABC withAC BC and median CDProve: CD is the perpendicularbisector of AB.AD PuoorStatementReasuns1. AC BCMedian CD of AABC1.2. Dis the midpoint ofAB.2.3. Definition of midpoint4.3.4. ZA ZB6. ACAD ACBD6. ZCDA s 2CDB7, 2CDA andZCDBform a linear pair.5.7.8. Linear Pair Postulate9. Theorem 6110. Definition of perpen-dieular segments8.9.10. CD is perpendicularto AB.11.అ11.

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Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Isosceles Triangle (Theorem)

6. The median to the base of an isosceles triangle is the
perpendicular bisector of the base.
RESTATEMENT
Given: Isosceles triangle ABC with
AC BC and median CD
Prove: CD is the perpendicular
bisector of AB.
A
D

Puoor
Statement
Reasuns
1. AC BC
Median CD of AABC
1.
2. Dis the midpoint of
AB.
2.
3. Definition of midpoint
4.
3.
4. ZA ZB
6. ACAD ACBD
6. ZCDA s 2CDB
7, 2CDA andZCDB
form a linear pair.
5.
7.
8. Linear Pair Postulate
9. Theorem 61
10. Definition of perpen-
dieular segments
8.
9.
10. CD is perpendicular
to AB.
11.
అ
11.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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