J:(x1 plus zero over two comma y1 plus zero over two) JOparallelRN Definition of Parallel Lines MJO = mRN Transitive Property of Equality MRN = zero over x subscript two Subtraction
MRN = zero minus zero over x2 minus zero Substitution MJO = divided by x2 over two = 0 Division Y2 minus y1 over x2 minus x1 Slope Formula O:(x1 plus x2 over two comma y1 plus zero over two) Substitution J:(x1 plus zero over two comma y1 plus zero over two) Substitution X sub 1 plus x sub 2 all over 2, y sub 1 plus y sub 2 all over 2 Midpoint Formula
It states that a segment connecting the midpoints of two sides of a triangle is parallel to the third side and its length is equal to half the length of the third side. Therefore, angle 1 is congruent to angle 3. So the sum of angle 1 and angle 2 is equal to the sum of angle 2 and angle 3.īy the subtraction property of equality, angle 2 can be subtracted from both sides of the equation, proving that the measures of angle 1 and 3 are equal. And, by definition of supplementary angles, we know that angle 2 plus angle 3 is equal to 180.īy the transitive property of equality, since both the sum of angles 1 and 2 and the sum of angles 2 and 3 equal 180 degrees, you know that these sums must be equal to one another. Another pair of two angles that form a straight line are angles 2 and 3. The second step is very similar to the first. Therefore, angle 1 plus angle 2 is equal to 180. The first step is to point out that two angles that form a straight line sum to 180 degrees by the definition of supplementary angles. You are given an image of two intersecting segments and asked to prove that angle 1 is congruent to angle 3.īy looking at the image, you can see that the two intersecting segments form four angles.
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