Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
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Chapter 3.8, Problem 7PSB
To determine

To prove : The altitude of an equilateral triangle is also a median of the triangle.

Expert Solution & Answer
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Explanation of Solution

Given information : The following information has been given

The triangle is equilateral

Let’s assume an equilateral triangle ABC with base BC, and altitude AD

Formula used : All the sides and angles of an equilateral triangle are congruent

Proof : We know that for the triangles ABD and ACD,

  ADCADB=900

AD is the common chord

  ABAC (sides of equilateral triangle)

Thus, we can say that the two triangles are congruent by SAS property, now, we know that congruent triangles have congruent sides. Thus, we can say that

  BDCD

This can be said like D is the median of the line BC.

Hence, proved that altitude of an equilateral triangle is also a median of the triangle.

Chapter 3 Solutions

Geometry For Enjoyment And Challenge

Ch. 3.2 - Prob. 6PSACh. 3.2 - Prob. 7PSACh. 3.2 - Prob. 8PSACh. 3.2 - Prob. 9PSACh. 3.2 - Prob. 10PSACh. 3.2 - Prob. 11PSACh. 3.2 - Prob. 12PSACh. 3.2 - Prob. 13PSACh. 3.2 - Prob. 14PSACh. 3.2 - Prob. 15PSACh. 3.2 - Prob. 16PSACh. 3.2 - Prob. 17PSBCh. 3.2 - Prob. 18PSBCh. 3.2 - Prob. 19PSBCh. 3.2 - Prob. 20PSBCh. 3.2 - Prob. 21PSBCh. 3.2 - Prob. 22PSBCh. 3.2 - Prob. 23PSBCh. 3.2 - Prob. 24PSBCh. 3.2 - Prob. 25PSBCh. 3.2 - Prob. 26PSCCh. 3.2 - Prob. 27PSCCh. 3.2 - Prob. 28PSCCh. 3.3 - Prob. 1PSACh. 3.3 - Prob. 2PSACh. 3.3 - Prob. 3PSACh. 3.3 - Prob. 4PSACh. 3.3 - Prob. 5PSACh. 3.3 - Prob. 6PSACh. 3.3 - Prob. 7PSACh. 3.3 - Prob. 8PSACh. 3.3 - Prob. 9PSACh. 3.3 - Prob. 10PSACh. 3.3 - Prob. 11PSACh. 3.3 - Prob. 12PSBCh. 3.3 - Prob. 13PSBCh. 3.3 - Prob. 14PSBCh. 3.3 - Prob. 15PSBCh. 3.3 - Prob. 16PSBCh. 3.3 - Prob. 17PSBCh. 3.3 - Prob. 18PSBCh. 3.3 - Prob. 19PSBCh. 3.3 - Prob. 20PSBCh. 3.3 - Prob. 21PSCCh. 3.3 - Prob. 22PSCCh. 3.3 - Prob. 23PSCCh. 3.4 - Prob. 1PSACh. 3.4 - Prob. 2PSACh. 3.4 - Prob. 3PSACh. 3.4 - Prob. 4PSACh. 3.4 - Prob. 5PSACh. 3.4 - Prob. 6PSACh. 3.4 - Prob. 7PSACh. 3.4 - Prob. 8PSBCh. 3.4 - Prob. 9PSBCh. 3.4 - Prob. 10PSBCh. 3.4 - Prob. 11PSBCh. 3.4 - Prob. 12PSCCh. 3.4 - Prob. 13PSCCh. 3.4 - Prob. 14PSCCh. 3.4 - Prob. 15PSCCh. 3.5 - Prob. 1PSACh. 3.5 - Prob. 2PSACh. 3.5 - Prob. 3PSACh. 3.5 - Prob. 4PSACh. 3.5 - Prob. 5PSACh. 3.5 - Prob. 6PSBCh. 3.5 - Prob. 7PSBCh. 3.5 - Prob. 8PSBCh. 3.5 - Prob. 9PSBCh. 3.5 - Prob. 10PSBCh. 3.5 - Prob. 11PSBCh. 3.5 - Prob. 12PSCCh. 3.5 - Prob. 13PSCCh. 3.5 - Prob. 14PSCCh. 3.6 - Prob. 1PSACh. 3.6 - Prob. 2PSACh. 3.6 - Prob. 3PSACh. 3.6 - Prob. 4PSACh. 3.6 - Prob. 5PSACh. 3.6 - Prob. 6PSACh. 3.6 - Prob. 7PSBCh. 3.6 - Prob. 8PSBCh. 3.6 - Prob. 9PSBCh. 3.6 - Prob. 10PSBCh. 3.6 - Prob. 11PSBCh. 3.6 - Prob. 12PSBCh. 3.6 - Prob. 13PSBCh. 3.6 - Prob. 14PSCCh. 3.6 - Prob. 15PSCCh. 3.6 - Prob. 16PSCCh. 3.7 - Prob. 1PSACh. 3.7 - Prob. 2PSACh. 3.7 - Prob. 3PSACh. 3.7 - Prob. 4PSACh. 3.7 - Prob. 5PSACh. 3.7 - Prob. 6PSACh. 3.7 - Prob. 7PSACh. 3.7 - Prob. 8PSACh. 3.7 - Prob. 9PSACh. 3.7 - Prob. 10PSACh. 3.7 - Prob. 11PSACh. 3.7 - Prob. 12PSBCh. 3.7 - Prob. 13PSBCh. 3.7 - Prob. 14PSBCh. 3.7 - Prob. 15PSBCh. 3.7 - Prob. 16PSBCh. 3.7 - Prob. 17PSBCh. 3.7 - Prob. 18PSBCh. 3.7 - Prob. 19PSBCh. 3.7 - Prob. 20PSBCh. 3.7 - Prob. 21PSBCh. 3.7 - Prob. 22PSCCh. 3.7 - Prob. 23PSCCh. 3.7 - Prob. 24PSCCh. 3.7 - Prob. 25PSCCh. 3.8 - Prob. 1PSACh. 3.8 - Prob. 2PSACh. 3.8 - Prob. 3PSACh. 3.8 - Prob. 4PSACh. 3.8 - Prob. 5PSACh. 3.8 - Prob. 6PSACh. 3.8 - Prob. 7PSBCh. 3.8 - Prob. 8PSBCh. 3.8 - Prob. 9PSBCh. 3.8 - Prob. 10PSBCh. 3.8 - Prob. 11PSBCh. 3.8 - Prob. 12PSBCh. 3.8 - Prob. 13PSBCh. 3.8 - Prob. 14PSBCh. 3.8 - Prob. 15PSBCh. 3.8 - Prob. 16PSCCh. 3.8 - Prob. 17PSCCh. 3.8 - Prob. 18PSDCh. 3 - Prob. 1RPCh. 3 - Prob. 2RPCh. 3 - Prob. 3RPCh. 3 - Prob. 4RPCh. 3 - Prob. 5RPCh. 3 - Prob. 6RPCh. 3 - Prob. 7RPCh. 3 - Prob. 8RPCh. 3 - Prob. 9RPCh. 3 - Prob. 10RPCh. 3 - Prob. 11RPCh. 3 - Prob. 12RPCh. 3 - Prob. 13RPCh. 3 - Prob. 14RPCh. 3 - Prob. 15RPCh. 3 - Prob. 16RPCh. 3 - Prob. 17RPCh. 3 - Prob. 18RPCh. 3 - Prob. 1CRCh. 3 - Prob. 2CRCh. 3 - Prob. 3CRCh. 3 - Prob. 4CRCh. 3 - Prob. 5CRCh. 3 - Prob. 6CRCh. 3 - Prob. 7CRCh. 3 - Prob. 8CRCh. 3 - Prob. 9CRCh. 3 - Prob. 10CRCh. 3 - Prob. 11CRCh. 3 - Prob. 12CRCh. 3 - Prob. 13CRCh. 3 - Prob. 14CRCh. 3 - Prob. 15CRCh. 3 - Prob. 16CRCh. 3 - Prob. 17CRCh. 3 - Prob. 18CRCh. 3 - Prob. 19CRCh. 3 - Prob. 20CRCh. 3 - Prob. 21CRCh. 3 - Prob. 22CRCh. 3 - Prob. 23CRCh. 3 - Prob. 24CR
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