Given: <1 and <2 are complementary. <1 is congruent to <3 and <2 is congruent to <4. Prove: <3 and <4 are complementary.

Question

 Please help!!

Answer 1

Given:

 

  angle1 + angle2 = 90;

 

  angle1 = angle3;

 

 angle2 = angle4;

 

Since angle1 + angle2 = 90  is given

 

        angle3 + angle4 = 90 by substituting angle1 = angle3 and angle2=angle4.

 

  Therefore angle3 and angle4 are complementary since they add up to 90,  by definition of complementary angles.

 

End of proof

 

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STEP / REASON FORM

 

 

1) angle1 and angle2 are complmentary :  given

2) angle1 + angle2 = 90   : definition of complementary angles

3) angle1 = angle3 and angle2 = angle4 : given

3) angle3 + angle4 = 90 : substitution of angle1 and angle2 with angle3 and angle4, respecitvely

4) angle 3 and angle4 are complementary : definition of complementary angles