   Chapter 3.3, Problem 34E ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Suppose that Δ A B C ≅ Δ D E F . Also, A X ¯ is the median from A to B C ¯ and D Y ¯ is the median from D to E F ¯ . Are these corresponding medians of congruent triangles congruent? Exercises 35, 36

To determine

To prove:

The median AX¯ is congruent to median DY¯.

Explanation

Approach:

(1) Corresponding parts of congruent triangles are congruent (CPCTC).

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

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

Calculation:

AX¯ is the median from A to BC¯ and DY¯ is the median from D to EF¯. Since, ΔABCΔDEF.

Consider the given figure.

Figure (1)

Prove of the given statement is as follows.

 Proof Statement Reasons (1) ΔABC≅ΔDEF (1) Given

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