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20. Write a two-column proof:
Given: BAC = DAC, DCA = BCA
Prove: BC = CD

20 Write A Twocolumn Proof Given BAC DAC DCA BCA Prove BC CD class=

Sagot :

Given:

[tex]\angle BAC\cong \angle DAC, \angle DCA\cong \angle BCA[/tex]

To prove:

[tex]\overline{BC} \cong \overline{CD}[/tex]

Solution:

The two-column proof is:

Statement                                        Reason

1. [tex]\angle BAC\cong \angle DAC[/tex]                            1. Given

2. [tex]\angle BCA\cong \angle DCA[/tex]                           2. Given

3. [tex]\overline{AC} \cong \overline{AC}[/tex]                                      3. Common side

4. [tex]\Delta ABC\cong \Delta ADC[/tex]                          4. ASA congruent postulate

5. [tex]\overline{BC} \cong \overline{CD}[/tex]                                     5. CPCTC

Hence proved.

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