Chapter 3.3, Problem 44E

### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Chapter
Section

### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 44 to 44, explain why each statement is true.The altitude from the vertex of an isosceles triangle is also the median to the base of the triangle.

To determine

To explain:

The altitude from the vertex of an isosceles triangle is also the median to the base of the triangle.

Explanation

(1) If two angles of one triangle are congruent to two angles of second triangle, then the third angle of both triangles are congruent.

(2) If two angles and the included side of one triangle are congruent to two angles and the included sides of a second triangle, then the triangles are congruent (ASA).

(3) Median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

Given:

An isosceles Î”ABC is given with altitude ADÂ¯ and ABÂ¯â‰…ACÂ¯.

Figure (1)

Approach:

Consider the Î”ABC with altitude ADÂ¯.

Altitude ADÂ¯ is perpendicular to BCÂ¯.

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