   Chapter 6.3, Problem 30E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 27 to 30, provide a paragraph proof.Given: A B ¯ ≅ C D ¯     i n     ⊙ P Prove: Δ A B D ≅ Δ C D B . To determine

To find:

To prove ΔABDΔCDB.

Explanation

Given that, AB¯CD¯inP.

To prove ΔABDΔCDB

The diagrammatic representation is given below,

From the above figure shows that DAB,ABD,BCD,CDB have the vertex on the circle.

We know that inscribed angle is half of the arc measure. That is,

mDAB=mDB^2

mBCD=mDB^2

mDAB=mBC^2

Given that AB¯CD¯inP therefore, mADB^=mDBC^

Then add the arc to get the following,

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