Geometry, please answer question ASAP

Mathematics

1 answer:

Pepsi [2]3 years ago

7 0

Answer:

Figures A,D are polygons.

Reason:

Polygon is a closed figure with atleast three strange lines and angles.

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PLEASE HELP<br> (look at pictures)

Vladimir [108]

<h2>Answer:</h2>

This is a theorem called Converse of Alternate Exterior Angles that states that <em>if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel</em>. Moreover, this theorem is based upon the corresponding Angles Converse Postulate that states that<em> if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. </em>We don't need to prove this postulate, it's assume to be true. So our goal is to get corresponding angles congruent in order to use the corresponding Angles Converse Postulate,

Reason: Given

Statement: $\angle1\cong\angle2$

Reason: Def of vertical $\angle s$

Statement: $\angle1\:and\:\angle3 \ are \ vertical$

Reason: Def of vertical $\angle s$

Statement: $\angle1\cong\angle3$

Reason: Transitive Property

Statement: $\angle2\cong\angle3$

Reason: corresponding Angles Converse Postulate

Statement: $p\parallel q$

6 0

2 years ago

Write the rectangular equation (x+5) 2 + y 2 = 25 in polar form.

Serjik [45]

Answer:

r = -10*cos(t)

Step-by-step explanation:

To write the rectangular equation in polar form we need to replace x and y by:

$x=r*cos(t)\\y=r*sin(t)$

Replacing on the original equation, we get:

$(x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25$

Using the identity $sin^2(t)+cos^2(t)=1$ and solving for r, we get that the polar form of the equation is:

$(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)$