Answer :

olayemiolakunle65

Answer:

Step-by-step explanation:

16. m<CAD + m<DAE = [tex]90^{O}[/tex]  -  Definition of complementary angles

18.  m<CAD + m<DAE = m<CAE =  [tex]90^{O}[/tex]   -  Substitution property

20. m<CAE =   [tex]90^{O}[/tex]                      -  Definition of perpendicular

21. AE ⊥ AC  -  AE is tangent to circle C

To prove that AE is tangent to C. Given that CA is the radius of circle C,

Then,

m<CAD + m<DAE = [tex]90^{O}[/tex]

So that,

AE ⊥ AC

Thus, AE is tangent to C.

sarbear97

Answer:

(Statement ------> Reason)

1 )  Circle C is constructed so that CD = DE = AD; Line segment CA is a radius of circle C. -------> Given

2) Line segment CD is congruent to line segment DE; line segment DE is congruent to line segment AD --------> Definition of congruence

3) Triangle ACD is an isosceles triangle; Triangle ADE is an isosceles triangle. --------> Isosceles triangle theorem

4) m<CAD + m<DCA + m<ADC = 180 degrees; m<DAE = m<AED + m<EDA = 180 degrees ---------> Substitution property

5) CD = DE --------> Isosceles triangle theorem

6) m<CAD = m<DCA; m<CAE = m<AED --------> Definition of congruence

7) m<CAD + m<CAD + m<ADC = 180 degrees; m<DAE = m<DAE + m<EDA = 180 degrees -------> Substitution property

8) 2(m<CAD) + m<ADC = 180 degrees; 2(m<DAE) + m<EDA = 180 degrees --------> Addition

9) m<ADC = 180 degrees - 2(m<CAD); m<EDA = 180 degrees - 2(m<DAE) -------> Addition subtraction property

10) Angle ADC and Angle EDA are a linear pair. ----------> Linear pair postulate

11) Angle ADC + Angle EDA ---------> Linear pair postulate

12) m<ADC + m<EDA = 180 degrees -------> Definition of supplementary angles

13) 180 degrees - 2(m<CAD) + 180 degrees - 2(m<DAE) = 180 degrees -------> Substitution property

14) 360 degrees - 2(m<CAD) - 2(m<DAE) = 180 degrees -------> Addition

15) -2(m<CAD) - 2(m<DAE) = -180 degrees -----------> Subtraction property

16) m<CAD + m<DAE = 90 degrees ----------> Definition of complementary angles

17) m<CAD + m<DAE = m<CAE -----------> Angle addition postulate

18) m<CAD + m<DAE = m<CAE = 90 degrees ------> Substitution property

19) Angle CAE is a right angle ------> Definition of right angle

20) m<CAE = 90 degrees -------> Definition of perpendicular

21) Line segment AE is tangent to circle C. -------> AE ⊥ AC

Step-by-step explanation:

I'm not sure if the reason for #9 is correct, but that's what someone else in a different answer said, so I went ahead and put it.

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