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 15, Problem 20RP
To determine

To Justify: The median of triangle is half of the sum of its adjacent sides.

Expert Solution & Answer
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Explanation of Solution

Given:

  InΔABCAM is median on BCBM=MC

Formula Used:

Triangle-Inequality Theorem: It states that sum of two sides of a triangle is always greater than the third.

SAS Congruence: It states that two triangle will be congruent if two adjacent sides and joining angle are congruent to other triangle.

Calculation:

  Geometry For Enjoyment And Challenge, Chapter 15, Problem 20RP

  InΔABCAM is median on BCBM=MCExtend AM to Psuch thatAM¯MP¯Join to form quadrilateral ABPCAM=MPMC=BMAMC=BMP (Vertically opposite angle)ΔAMCΔBMP (SAS Congruence Rule)AP<AB+BPAM+MP<AB+AC2AM<AB+ACAM<12(AB+BC)

Conclusion:

Hence, Proved.

Chapter 15 Solutions

Geometry For Enjoyment And Challenge

Ch. 15.1 - Prob. 11PSBCh. 15.1 - Prob. 12PSBCh. 15.1 - Prob. 13PSBCh. 15.1 - Prob. 14PSCCh. 15.1 - Prob. 15PSCCh. 15.1 - Prob. 16PSCCh. 15.1 - Prob. 17PSCCh. 15.1 - Prob. 18PSCCh. 15.1 - Prob. 19PSCCh. 15.1 - Prob. 20PSDCh. 15.2 - Prob. 1PSACh. 15.2 - Prob. 2PSACh. 15.2 - Prob. 3PSACh. 15.2 - Prob. 4PSACh. 15.2 - Prob. 5PSACh. 15.2 - Prob. 6PSACh. 15.2 - Prob. 7PSBCh. 15.2 - Prob. 8PSBCh. 15.2 - Prob. 9PSBCh. 15.2 - Prob. 10PSBCh. 15.2 - Prob. 11PSBCh. 15.2 - Prob. 12PSBCh. 15.2 - Prob. 13PSBCh. 15.2 - Prob. 14PSBCh. 15.2 - Prob. 15PSBCh. 15.2 - Prob. 16PSBCh. 15.2 - Prob. 17PSBCh. 15.2 - Prob. 18PSBCh. 15.2 - Prob. 19PSBCh. 15.2 - Prob. 20PSCCh. 15.2 - Prob. 21PSCCh. 15.2 - Prob. 22PSCCh. 15.2 - Prob. 23PSCCh. 15.2 - Prob. 24PSCCh. 15.2 - Prob. 25PSCCh. 15.3 - Prob. 1PSACh. 15.3 - Prob. 2PSACh. 15.3 - Prob. 3PSACh. 15.3 - Prob. 4PSACh. 15.3 - Prob. 5PSACh. 15.3 - Prob. 6PSACh. 15.3 - Prob. 7PSACh. 15.3 - Prob. 8PSBCh. 15.3 - Prob. 9PSBCh. 15.3 - Prob. 10PSBCh. 15.3 - Prob. 11PSBCh. 15.3 - Prob. 12PSBCh. 15.3 - Prob. 13PSBCh. 15.3 - Prob. 14PSBCh. 15.3 - Prob. 15PSBCh. 15.3 - Prob. 16PSBCh. 15.3 - Prob. 17PSBCh. 15.3 - Prob. 18PSBCh. 15.3 - Prob. 19PSBCh. 15.3 - Prob. 20PSCCh. 15.3 - Prob. 21PSCCh. 15.3 - Prob. 22PSCCh. 15.3 - Prob. 23PSCCh. 15.3 - Prob. 24PSCCh. 15.3 - Prob. 25PSCCh. 15.3 - Prob. 26PSCCh. 15 - Prob. 1RPCh. 15 - Prob. 2RPCh. 15 - Prob. 3RPCh. 15 - Prob. 4RPCh. 15 - Prob. 5RPCh. 15 - Prob. 6RPCh. 15 - Prob. 7RPCh. 15 - Prob. 8RPCh. 15 - Prob. 9RPCh. 15 - Prob. 10RPCh. 15 - Prob. 11RPCh. 15 - Prob. 12RPCh. 15 - Prob. 13RPCh. 15 - Prob. 14RPCh. 15 - Prob. 15RPCh. 15 - Prob. 16RPCh. 15 - Prob. 17RPCh. 15 - Prob. 18RPCh. 15 - Prob. 19RPCh. 15 - Prob. 20RPCh. 15 - Prob. 21RPCh. 15 - Prob. 22RPCh. 15 - Prob. 23RPCh. 15 - Prob. 24RPCh. 15 - Prob. 25RPCh. 15 - Prob. 1CRCh. 15 - Prob. 2CRCh. 15 - Prob. 3CRCh. 15 - Prob. 4CRCh. 15 - Prob. 5CRCh. 15 - Prob. 6CRCh. 15 - Prob. 7CRCh. 15 - Prob. 8CRCh. 15 - Prob. 9CRCh. 15 - Prob. 10CRCh. 15 - Prob. 11CRCh. 15 - Prob. 12CRCh. 15 - Prob. 13CRCh. 15 - Prob. 14CRCh. 15 - Prob. 15CRCh. 15 - Prob. 16CRCh. 15 - Prob. 17CRCh. 15 - Prob. 18CRCh. 15 - Prob. 19CRCh. 15 - Prob. 20CRCh. 15 - Prob. 21CRCh. 15 - Prob. 22CRCh. 15 - Prob. 23CRCh. 15 - Prob. 24CRCh. 15 - Prob. 25CRCh. 15 - Prob. 26CRCh. 15 - Prob. 27CRCh. 15 - Prob. 28CRCh. 15 - Prob. 29CRCh. 15 - Prob. 30CRCh. 15 - Prob. 31CRCh. 15 - Prob. 32CRCh. 15 - Prob. 33CRCh. 15 - Prob. 34CRCh. 15 - Prob. 35CRCh. 15 - Prob. 36CRCh. 15 - Prob. 37CRCh. 15 - Prob. 38CRCh. 15 - Prob. 39CRCh. 15 - Prob. 40CRCh. 15 - Prob. 41CRCh. 15 - Prob. 42CRCh. 15 - Prob. 43CRCh. 15 - Prob. 44CRCh. 15 - Prob. 45CRCh. 15 - Prob. 46CRCh. 15 - Prob. 47CRCh. 15 - Prob. 48CRCh. 15 - Prob. 49CRCh. 15 - Prob. 50CR
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