Michael and derrick each completed a separate proof to show that corresponding angles akg and elk are congruent. who completed the proof incorrectly? explain

answer:

Michael's Proof is incorrect

Step-by-step explanation:

In Michael's proof, he messed up on 2. This is because he set the wrong angles congruent to each other. He said that angle AKG is congruent to angle AKL, but if you were to look at the transversal, you will see that the angles he gave are linear pairs and not vertical angles, which is incorrect.

answer:

Step-by-step explanation:

definition: a circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. the a line segment from the center of the circle to any point on the circle is a radius of the circle. by definition of a circle, all radii have the same length.

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

to ensure that the figure inside the circle (inscribed) is regular, we simply have to divide the circle with degrees measuring depending on the number of sides required. 

one of the differences between laura's construction and gavin's construction is that laura will have to divide the circle by four equal degrees in order make the inscribed square while gavin will have to divide the circle by six equal measurements to be able to form the inscribed hexagon. 

1. angles 2, 3 and angles 1,3 are complementary angles(given)

2. to prove :

since angles 2, 3 and angles 1,3 are complementary.

when angles are complementary, then the sum of the measures of angles is 90 degrees.

so,   and   (definition of complementary angles)

3.   (substitution)

4.   (subtraction property of equality)

step-by-step explanation:

Michael

Step-by-step explanation:

Angles AKG and BKL are vertically opposite angles.

Angles AKG and AKL are supplementary angles, not vertically opposite angles.

Therefore, Derrick's proof is correct. Michael's is incorrect

Michael is the one whose proof was completed incorrectly.

Step-by-step explanation:

The complete Question, the image of the angles being analysed and their respective proofs are presented in the attached image.

Michael proves that

1) Line AB is parallel to line EF with a transversal line GF (Given)

2) Angle AKG = Angle AKL (Vertically opposite angles are equal)

3) Angle BKL = Angle ELK (Alternate angles are equal)

4) Angle AKG = Angle ELK (Transitive property)

Derrick's Proof

1) Line AB is parallel to line EF with a transversal line GF (Given)

2) Angle AKG = Angle BKL (Vertically opposite angles are equal)

3) Angle BKL = Angle ELK (Alternate angles are equal)

4) Angle AKG = Angle ELK (Transitive property)

Derrick's Proof, from the first statement to the last, is entirely, mathematically correct and he establishes the transitive property that

Angle AKG = Angle BKL = Angle ELK

Hence, Angle AKG = Angle ELK

But Michael makes his own mistake on the second statement.

He says, Angle AKG = Angle AKL (Vertically opposite angles are equal) which is not mathematically true.

Angle AKG and Angle AKL are supplementary angles that sum up to 180° because they both make up the angle on the straight line GJ at the point K.

Furthermore, this makes his transitive claim not correct, because at the end of the day, he will obtain

Angle AKG = Angle AKL

Angle BKL = Angle ELK

So, Angle AKG ≠ Angle ELK with this proof.

It's either he made the mathematical error or he actually made a typographical error and wrote angle AKL in that 2nd statement instead of angle BKL because the rest of his proof seem to be on point.

Either ways, Michael's proof is the proof that is completed incorrectly.

Hope this Helps!!!

see below

Step-by-step explanation:

Michael is incorrect

AKG and AKL are not vertical angles

Why? Check out the diagram below. Michael makes a mention that AKG and AKL are vertical angles. This is not true as the angles are actually a linear pair (they are adjacent and supplementary), and they aren't the same measure unless we have a right angle.

Whereas Derrick's proof is correct. Angle AKG and angle BKL are vertical angles which are the same measure. Angle BKL and ELK are alternate interior angles that are congruent since AB || EF. So by the transitive property, we know that angle AKG is congruent to angle ELK.