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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

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

Does it follow from Exercise 30 that Δ A D E is also congruent to Δ C B E ? What can you conclude regarding A E ¯ and C E ¯ in the drawing? What can you conclude regarding D E ¯ a n d B E ¯ ?

To determine

To find:

To explain the ΔADE is also congruent to ΔCBE, also conclude regarding AE¯ and CE¯ in the drawing and regarding DE¯andBE¯.

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

mABD=mAD^2

mBCD=mDB^2

mDAB=mBC^2

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

Then add the arc to get the following,

mAD^+mDB^=mDB^+mBC^

mAD^=mBC^

By substituting the above

mDAB=mDB^2=mBCD

mDAB=mBCD

mABD=mAD^2=mBC^2=mCDB

mABD=mCDB

By using SAS postulate (two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent

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