Let us write vertices of the given rectangle are PQRS.
Where Q is (c,d) and S is (a,b).
a) Now, we need to find the coordinates of P and R points.
x-coordinate for P is a and y-coordinate of P is d.
<h3>Therefore P is (a,d).</h3>On the same way, x-coordinate for R is c and y-coordinate of R is b.
<h3>Therefore R is (d,b).</h3>b) <em>Width of the rectangle is difference of y-coordinates of P and S points</em>.
<h3>Therefore, width = b - d.</h3>
Linear pair angles, which are angles that together form a straight line are
supplementary angles.
The one that completed the proof incorrectly is <u>Becky</u>.
Reasons:
The two column proof is presented as follows;
Statement Reason
1. Segment GH intersects segment AB at K 1. Given
2. m∠AKG + m∠HKB = 180° 2.Definition of Supplementary Angles
m∠GKB + m∠HKB = 180°
3. m∠AKG + m∠HKB = m∠GKB + m∠HKB 3. Substitution property
4. m∠AKG = m∠HKB 4. Subtraction Property
The difference between Angie's Proof and Becky's Proof is in Statement 2.
Becky's proof is incorrect because the measure of angles m∠AKG and
m∠HKB and m∠GKB and m∠HKB are not given, therefore, the use of the
reason of Angle Addition Postulate in statement 2. is incorrect.
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