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 6.1, Problem 18PSC
To determine

To show that triangle AXD is an isosceles triangle.

Expert Solution & Answer
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Answer to Problem 18PSC

  ΔAXD is an isosceles  triangle.

Explanation of Solution

Given information:

  ΔABC    ΔDBC  

Formula used:

The below properties are used:

Two triangles are congruent by SAS congruence rule.

If two sides of a triangle are congruent, the triangle is isosceles.

Proof:

It is given that,

  ΔABC    ΔDBC  

  Geometry For Enjoyment And Challenge, Chapter 6.1, Problem 18PSC

As corresponding parts of congruent triangles are congruent, we get

  ABC   DBC

As corresponding parts of congruent triangles are congruent, we get

  AB¯   DB¯

By reflexive property, we get

  BX¯   BX¯

By SAS congruence rule, we get

  ΔABX    ΔDBX  

As corresponding parts of congruent triangles are congruent, we get

  AX¯   DX¯

If two sides of a triangle are congruent, the triangle is isosceles.

  ΔAXD is an isosceles triangle .

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Geometry For Enjoyment And Challenge

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